path stringlengths 11 71 | content stringlengths 75 124k |
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Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Unital.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Quasispectrum
import Mathlib.Algebra.Algebra.Spectrum
import Mathlib.Algebra.Star.Order
import Mathlib.Topology.Algebra.Polynomial
import... |
Analysis\CStarAlgebra\ContinuousFunctionalCalculus\Unitary.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Tactic.Peel
import Mathlib.Analysis.CStarAlgebra.ContinuousFunctionalCalculus.Unital
import Mathlib.Analysis.Complex.Basic
/-! # Conditions on unitary e... |
Analysis\Distribution\AEEqOfIntegralContDiff.lean | /-
Copyright (c) 2023 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Geometry.Manifold.PartitionOfUnity
import Mathlib.Geometry.Manifold.Metrizable
import Mathlib.MeasureTheory.Function.AEEqOfIntegral
/-!
# Functi... |
Analysis\Distribution\FourierSchwartz.lean | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Distribution.SchwartzSpace
import Mathlib.Analysis.Fourier.FourierTransformDeriv
import Mathlib.Analysis.Fourier.Inversion
/-!
# Fourie... |
Analysis\Distribution\SchwartzSpace.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.Calculus.ContDiff.Bounds
import Mathlib.Analysis.Calculus.IteratedDeriv.Defs
import Mathlib.Analysis.Calculus.LineDeriv.Basic
import Mathlib.Analysi... |
Analysis\Fourier\AddCircle.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, David Loeffler
-/
import Mathlib.Analysis.SpecialFunctions.ExpDeriv
import Mathlib.Analysis.SpecialFunctions.Complex.Circle
import Mathlib.Analysis.InnerProductSpace.... |
Analysis\Fourier\FourierTransform.lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.Complex.Circle
import Mathlib.MeasureTheory.Group.Integral
import Mathlib.MeasureTheory.Integral.SetIntegral
import Mathlib.MeasureTheory.Meas... |
Analysis\Fourier\FourierTransformDeriv.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Alex Kontorovich, David Loeffler, Heather Macbeth, Sébastien Gouëzel
-/
import Mathlib.Analysis.Calculus.ParametricIntegral
import Mathlib.Analysis.Fourier.AddCircle
import Mathlib.Ana... |
Analysis\Fourier\Inversion.lean | /-
Copyright (c) 2024 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.MeasureTheory.Integral.PeakFunction
import Mathlib.Analysis.SpecialFunctions.Gaussian.FourierTransform
/-!
# Fourier inversion formula
In a fin... |
Analysis\Fourier\PoissonSummation.lean | /-
Copyright (c) 2023 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.Fourier.AddCircle
import Mathlib.Analysis.Fourier.FourierTransform
import Mathlib.Analysis.PSeries
import Mathlib.Analysis.Distribution.Schwar... |
Analysis\Fourier\RiemannLebesgueLemma.lean | /-
Copyright (c) 2022 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.Fourier.FourierTransform
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.InnerProductSpace.EuclideanDist
import Mathlib... |
Analysis\Fourier\ZMod.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.SpecialFunctions.Complex.CircleAddChar
import Mathlib.Analysis.Fourier.FourierTransform
import Mathlib.NumberTheory.DirichletCharacter.GaussSu... |
Analysis\FunctionalSpaces\SobolevInequality.lean | /-
Copyright (c) 2024 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
import Mathlib.Analysis.Calculus.Deriv.Pi
import Mathlib.Analysis.InnerProductSpace.EuclideanDist
import Mathlib.Analysis.InnerProductSpace.NormP... |
Analysis\InnerProductSpace\Adjoint.lean | /-
Copyright (c) 2021 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Adjoint of operators on Hilbert spaces
Given ... |
Analysis\InnerProductSpace\Basic.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis
-/
import Mathlib.Algebra.DirectSum.Module
import Mathlib.Algebra.Module.LinearMap.Basic
import Mathlib.Algebra.QuadraticDiscriminant
i... |
Analysis\InnerProductSpace\Calculus.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Analysis.SpecialFunctions.Sqrt
import Mathlib.Analysis.NormedSpace.HomeomorphBall
/-!
# Calculus in i... |
Analysis\InnerProductSpace\ConformalLinearMap.lean | /-
Copyright (c) 2021 Yourong Zang. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yourong Zang
-/
import Mathlib.Analysis.NormedSpace.ConformalLinearMap
import Mathlib.Analysis.InnerProductSpace.Basic
/-!
# Conformal maps between inner product spaces
In an inner pro... |
Analysis\InnerProductSpace\Dual.lean | /-
Copyright (c) 2020 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Projection
import Mathlib.Analysis.Normed.Module.Dual
/-!
# The Fréchet-Riesz representation theorem
We consider an inne... |
Analysis\InnerProductSpace\EuclideanDist.lean | /-
Copyright (c) 2021 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.InnerProductSpace.Calculus
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Topology.MetricSpace.ProperSpace.Lemmas
/-!
# Eucl... |
Analysis\InnerProductSpace\GramSchmidtOrtho.lean | /-
Copyright (c) 2022 Jiale Miao. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jiale Miao, Kevin Buzzard, Alexander Bentkamp
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.LinearAlgebra.Matrix.Block
/-!
# Gram-Schmidt Orthogonalization and Orthonor... |
Analysis\InnerProductSpace\l2Space.lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Projection
import Mathlib.Analysis.Normed.Lp.lpSpace
import Mathlib.Analysis.InnerProductSpace.PiL2
/-!
# Hilbert sum of ... |
Analysis\InnerProductSpace\LaxMilgram.lean | /-
Copyright (c) 2022 Daniel Roca González. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Daniel Roca González
-/
import Mathlib.Analysis.InnerProductSpace.Dual
/-!
# The Lax-Milgram Theorem
We consider a Hilbert space `V` over `ℝ`
equipped with a bounded bilinear f... |
Analysis\InnerProductSpace\LinearPMap.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
import Mathlib.Topology.Algebra.Module.Basic
/-!
# Partially defined linear operators on Hilbert spaces
We will develop... |
Analysis\InnerProductSpace\MeanErgodic.lean | /-
Copyright (c) 2023 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.InnerProductSpace.Projection
import Mathlib.Dynamics.BirkhoffSum.NormedSpace
/-!
# Von Neumann Mean Ergodic Theorem in a Hilbert Space
In ... |
Analysis\InnerProductSpace\NormPow.lean | /-
Copyright (c) 2024 Floris van Doorn. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Floris van Doorn, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Calculus
import Mathlib.Analysis.Normed.Module.Dual
import Mathlib.Analysis.SpecialFunctions.Pow.Deriv
... |
Analysis\InnerProductSpace\OfNorm.lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Topology.Algebra.Algebra
import Mathlib.Analysis.InnerProductSpace.Basic
/-!
# Inner product space derived from a norm
This file defines an `InnerP... |
Analysis\InnerProductSpace\Orientation.lean | /-
Copyright (c) 2022 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.GramSchmidtOrtho
import Mathlib.LinearAlgebra.Orientation
/-!
# Orientations of real inner product spaces.
Th... |
Analysis\InnerProductSpace\Orthogonal.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Sébastien Gouëzel, Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.LinearAlgebra.SesquilinearForm
/-!
# Orthogonal complements of submo... |
Analysis\InnerProductSpace\PiL2.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Sébastien Gouëzel, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Projection
import Mathlib.Analysis.Normed.Lp.PiLp
import Mathlib.LinearAlgebra.FiniteDimensi... |
Analysis\InnerProductSpace\Positive.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Analysis.InnerProductSpace.Adjoint
/-!
# Positive operators
In this file we define positive operators in a Hilbert space. We follow Bourbaki's ch... |
Analysis\InnerProductSpace\ProdL2.lean | /-
Copyright (c) 2023 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Analysis.Normed.Lp.ProdLp
/-!
# `L²` inner product space structure on products of inner product spaces
The `... |
Analysis\InnerProductSpace\Projection.lean | /-
Copyright (c) 2019 Zhouhang Zhou. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Zhouhang Zhou, Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Analysis.InnerProductSpace.Orthogonal
import Mathlib.Analysis.InnerProductSpace.Sy... |
Analysis\InnerProductSpace\Rayleigh.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth, Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Calculus
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.InnerProductSpace.Adjoint... |
Analysis\InnerProductSpace\Spectrum.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Rayleigh
import Mathlib.Analysis.InnerProductSpace.PiL2
import Mathlib.Algebra.DirectSum.Decomposition
import Mathlib.Line... |
Analysis\InnerProductSpace\Symmetric.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Frédéric Dupuis, Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Basic
import Mathlib.Analysis.Normed.Operator.Banach
import Mathlib.LinearAlgebra.Sesquilin... |
Analysis\InnerProductSpace\TwoDim.lean | /-
Copyright (c) 2022 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.InnerProductSpace.Orientation
import Mathlib.Data.Complex.FiniteDimensional
import Mathlib.Da... |
Analysis\InnerProductSpace\WeakOperatorTopology.lean | /-
Copyright (c) 2024 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.InnerProductSpace.Dual
import Mathlib.Analysis.Normed.Operator.WeakOperatorTopology
/-!
# The weak operator topology in Hilbert spaces
Th... |
Analysis\LocallyConvex\AbsConvex.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
import Mathlib.Analysis.LocallyConvex.WithSeminorms
import Mathlib.Analysis.Convex.Gauge
/-!
# Absolutely convex set... |
Analysis\LocallyConvex\BalancedCoreHull.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.LocallyConvex.Basic
/-!
# Balanced Core and Balanced Hull
## Main definitions
* `balancedCore`: The largest balanced subset of a set `s`.
* `bala... |
Analysis\LocallyConvex\Barrelled.lean | /-
Copyright (c) 2023 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Analysis.LocallyConvex.WithSeminorms
import Mathlib.Topology.Semicontinuous
import Mathlib.Topology.Baire.Lemmas
/-!
# Barrelled spaces and the Ba... |
Analysis\LocallyConvex\Basic.lean | /-
Copyright (c) 2019 Jean Lo. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jean Lo, Bhavik Mehta, Yaël Dillies
-/
import Mathlib.Analysis.Convex.Basic
import Mathlib.Analysis.Convex.Hull
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Topology.Bornology.A... |
Analysis\LocallyConvex\Bounded.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.GroupTheory.GroupAction.Pointwise
import Mathlib.Analysis.LocallyConvex.Basic
import Mathlib.Analysis.LocallyConvex.BalancedCoreHull
import Mathlib.Analysis.... |
Analysis\LocallyConvex\ContinuousOfBounded.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.LocallyConvex.Bounded
import Mathlib.Analysis.RCLike.Basic
/-!
# Continuity and Von Neumann boundedness
This files proves that for `E` and `F... |
Analysis\LocallyConvex\Polar.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Kalle Kytölä
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.LinearAlgebra.SesquilinearForm
import Mathlib.Topology.Algebra.Module.WeakDual
/-!
# Polar set
In ... |
Analysis\LocallyConvex\StrongTopology.lean | /-
Copyright (c) 2022 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Topology.Algebra.Module.StrongTopology
import Mathlib.Topology.Algebra.Module.LocallyConvex
/-!
# Local convexity of the strong topology
In this ... |
Analysis\LocallyConvex\WeakDual.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Topology.Algebra.Module.WeakDual
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Analysis.LocallyConvex.WithSeminorms
/-!
# Weak Dual in Topologic... |
Analysis\LocallyConvex\WithSeminorms.lean | /-
Copyright (c) 2022 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Anatole Dedecker
-/
import Mathlib.Analysis.LocallyConvex.Bounded
import Mathlib.Analysis.Seminorm
import Mathlib.Data.Real.Sqrt
import Mathlib.Topology.Algebra.Equicontinuit... |
Analysis\Normed\MulAction.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Topology.MetricSpace.Algebra
import Mathlib.Analysis.Normed.Field.Basic
/-!
# Lemmas for `BoundedSMul` over normed additive groups
Lemmas which hold only i... |
Analysis\Normed\Algebra\Basic.lean | /-
Copyright (c) 2022 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Topology.Algebra.Module.CharacterSpace
import Mathlib.Analysis.Normed.Module.WeakDual
import Mathlib.Analysis.Normed.Algebra.Spectrum
/-!
# Normed a... |
Analysis\Normed\Algebra\Exponential.lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker, Eric Wieser
-/
import Mathlib.Analysis.Analytic.Basic
import Mathlib.Analysis.Complex.Basic
import Mathlib.Analysis.Normed.Field.InfiniteSum
import Mathlib.Data.Nat... |
Analysis\Normed\Algebra\MatrixExponential.lean | /-
Copyright (c) 2022 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Analysis.Normed.Algebra.Exponential
import Mathlib.Analysis.Matrix
import Mathlib.LinearAlgebra.Matrix.ZPow
import Mathlib.LinearAlgebra.Matrix.Hermitian
imp... |
Analysis\Normed\Algebra\QuaternionExponential.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Analysis.Quaternion
import Mathlib.Analysis.Normed.Algebra.Exponential
import Mathlib.Analysis.SpecialFunctions.Trigonometric.Series
/-!
# Lemmas about `Nor... |
Analysis\Normed\Algebra\Spectrum.lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Quasispectrum
import Mathlib.FieldTheory.IsAlgClosed.Spectrum
import Mathlib.Analysis.Complex.Liouville
import Mathlib.Analysis.Complex.P... |
Analysis\Normed\Algebra\TrivSqZeroExt.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Analysis.Normed.Algebra.Exponential
import Mathlib.Analysis.Normed.Lp.ProdLp
import Mathlib.Topology.Instances.TrivSqZeroExt
/-!
# Results on `TrivSqZeroExt... |
Analysis\Normed\Algebra\Unitization.lean | /-
Copyright (c) 2023 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Unitization
import Mathlib.Analysis.NormedSpace.OperatorNorm.Mul
/-!
# Unitization norms
Given a not-necessarily-unital normed `𝕜`-al... |
Analysis\Normed\Algebra\UnitizationL1.lean | /-
Copyright (c) 2024 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Algebra.Algebra.Unitization
import Mathlib.Analysis.Normed.Lp.ProdLp
/-! # Unitization equipped with the $L^1$ norm
In another file, the `Unitization �... |
Analysis\Normed\Field\Basic.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.Algebra.Algebra.NonUnitalSubalgebra
import Mathlib.Algebra.Algebra.Subalgebra.Basic
import Mathlib.Algebra.Order.Ring.Finset
import Mat... |
Analysis\Normed\Field\InfiniteSum.lean | /-
Copyright (c) 2021 Anatole Dedecker. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Anatole Dedecker
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Analysis.Normed.Group.InfiniteSum
import Mathlib.Topology.Algebra.InfiniteSum.Real
/-! # Multiplying tw... |
Analysis\Normed\Field\UnitBall.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import Mathlib.Analysis.Normed.Field.Basic
import Mathlib.Analysis.Normed.Group.BallSphere
/-!
# Algebraic structures on unit balls and spheres
I... |
Analysis\Normed\Group\AddCircle.lean | /-
Copyright (c) 2022 Oliver Nash. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Oliver Nash
-/
import Mathlib.Analysis.Normed.Group.Quotient
import Mathlib.Topology.Instances.AddCircle
/-!
# The additive circle as a normed group
We define the normed group structure... |
Analysis\Normed\Group\AddTorsor.lean | /-
Copyright (c) 2020 Joseph Myers. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Joseph Myers, Yury Kudryashov
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Analysis.Normed.Group.Submodule
import Mathlib.LinearAlgebra.AffineSpace.AffineSubspace
import ... |
Analysis\Normed\Group\BallSphere.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Heather Macbeth
-/
import Mathlib.Analysis.Normed.Group.Uniform
/-!
# Negation on spheres and balls
In this file we define `InvolutiveNeg` and `ContinuousNeg` insta... |
Analysis\Normed\Group\Basic.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Algebra.CharP.Defs
import Mathlib.Algebra.Group.Subgroup.Basic
import Mathlib.Analysis.Normed.Group.Seminorm
import Mathl... |
Analysis\Normed\Group\Bounded.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Topology.MetricSpace.Bounded
import Mathlib.Order.Filter.Pointwise
import Math... |
Analysis\Normed\Group\CocompactMap.lean | /-
Copyright (c) 2024 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Topology.ContinuousFunction.CocompactMap
import Mathlib.Topology.MetricSpace.Bounded
/-!
# Cocompact maps in nor... |
Analysis\Normed\Group\Completeness.lean | /-
Copyright (c) 2023 Frédéric Dupuis. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Frédéric Dupuis
-/
import Mathlib.Analysis.Normed.Group.Uniform
import Mathlib.Analysis.SpecificLimits.Basic
/-!
# Completeness of normed groups
This file includes a completeness c... |
Analysis\Normed\Group\Completion.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Analysis.Normed.Group.Uniform
import Mathlib.Topology.Algebra.GroupCompletion
import Mathlib.Topology.MetricSpace.Completion
/-!
# Completion of a nor... |
Analysis\Normed\Group\Constructions.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Algebra.Group.ULift
import Mathlib.Algebra.PUnitInstances.Algebra
import Mathlib.Analysis.Normed.Group.Basic
/-!
# Produ... |
Analysis\Normed\Group\ControlledClosure.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.Analysis.SpecificLimits.Normed
/-! # Extending a backward bound on a normed group homomorphism from a dense s... |
Analysis\Normed\Group\Hom.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin
-/
import Mathlib.Analysis.Normed.Group.Int
import Mathlib.Analysis.Normed.Group.Uniform
/-!
# Normed groups homomorphisms
This file gathers definitions and elementary... |
Analysis\Normed\Group\HomCompletion.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.Analysis.Normed.Group.Completion
/-!
# Completion of normed group homs
Given two (semi) normed groups `G` an... |
Analysis\Normed\Group\InfiniteSum.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Heather Macbeth, Johannes Hölzl, Yury Kudryashov
-/
import Mathlib.Algebra.BigOperators.Intervals
import Mathlib.Analysis.Normed.Group.Uniform
import Mathlib.Topo... |
Analysis\Normed\Group\Int.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Group.Basic
import Mathlib.Topology.Instances.Int
/-! # ℤ as a normed group -/
open NNReal
variable {... |
Analysis\Normed\Group\Lemmas.lean | /-
Copyright (c) 2022 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot
-/
import Mathlib.Analysis.Normed.Group.Uniform
import Mathlib.Topology.Instances.NNReal
/-!
# Further lemmas about normed groups
This file contains further lemmas abo... |
Analysis\Normed\Group\Pointwise.lean | /-
Copyright (c) 2021 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Group.Bounded
import Mathlib.Analysis.Normed.Group.Uniform
import Mathlib.Topology.MetricSpace.Thickening
/-!
# P... |
Analysis\Normed\Group\Quotient.lean | /-
Copyright (c) 2021 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Riccardo Brasca
-/
import Mathlib.Analysis.Normed.Module.Basic
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.RingTheory.Ideal.QuotientOperations
import Mathli... |
Analysis\Normed\Group\Rat.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Analysis.Normed.Group.Int
import Mathlib.Topology.Instances.Rat
/-! # ℚ as a normed group -/
namespace Rat
instance i... |
Analysis\Normed\Group\Seminorm.lean | /-
Copyright (c) 2022 María Inés de Frutos-Fernández, Yaël Dillies. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: María Inés de Frutos-Fernández, Yaël Dillies
-/
import Mathlib.Data.NNReal.Basic
import Mathlib.Tactic.GCongr.Core
/-!
# Group seminorms
This file defin... |
Analysis\Normed\Group\SemiNormedGrp.lean | /-
Copyright (c) 2021 Johan Commelin. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Johan Commelin, Riccardo Brasca
-/
import Mathlib.Analysis.Normed.Group.Constructions
import Mathlib.Analysis.Normed.Group.Hom
import Mathlib.CategoryTheory.Limits.Shapes.ZeroMorphisms... |
Analysis\Normed\Group\Submodule.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Algebra.Module.Submodule.LinearMap
import Mathlib.Analysis.Normed.Group.Basic
/-! # Submodules of normed groups -/
var... |
Analysis\Normed\Group\Tannery.lean | /-
Copyright (c) 2024 David Loeffler. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: David Loeffler
-/
import Mathlib.Analysis.RCLike.Basic
import Mathlib.Analysis.Normed.Group.InfiniteSum
/-!
# Tannery's theorem
Tannery's theorem gives a sufficient criterion for th... |
Analysis\Normed\Group\Uniform.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl, Yaël Dillies
-/
import Mathlib.Topology.Algebra.UniformGroup
import Mathlib.Topology.MetricSpace.Algebra
import Mathlib.Topology.MetricSpace.IsometricSM... |
Analysis\Normed\Group\ZeroAtInfty.lean | /-
Copyright (c) 2024 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Topology.ContinuousFunction.ZeroAtInfty
/-!
# ZeroAtInftyContinuousMapClass in normed additive groups
In this file we give a characterization of the predi... |
Analysis\Normed\Group\SemiNormedGrp\Completion.lean | /-
Copyright (c) 2021 Riccardo Brasca. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin
-/
import Mathlib.Analysis.Normed.Group.SemiNormedGrp
import Mathlib.CategoryTheory.Preadditive.AdditiveFunctor
import Mathlib.Analysis.Normed.Group.Ho... |
Analysis\Normed\Group\SemiNormedGrp\Kernels.lean | /-
Copyright (c) 2021 Scott Morrison. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Riccardo Brasca, Johan Commelin, Scott Morrison
-/
import Mathlib.Analysis.Normed.Group.SemiNormedGrp
import Mathlib.Analysis.Normed.Group.Quotient
import Mathlib.CategoryTheory.Limits... |
Analysis\Normed\Lp\LpEquiv.lean | /-
Copyright (c) 2022 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.Normed.Lp.lpSpace
import Mathlib.Analysis.Normed.Lp.PiLp
import Mathlib.Topology.ContinuousFunction.Bounded
/-!
# Equivalences among $L^p$ spac... |
Analysis\Normed\Lp\lpSpace.lean | /-
Copyright (c) 2021 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.MeanInequalities
import Mathlib.Analysis.MeanInequalitiesPow
import Mathlib.Analysis.SpecialFunctions.Pow.Continuity
import Mathlib.Data.Set... |
Analysis\Normed\Lp\PiLp.lean | /-
Copyright (c) 2020 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel, Jireh Loreaux
-/
import Mathlib.Analysis.MeanInequalities
import Mathlib.Data.Fintype.Order
import Mathlib.LinearAlgebra.Matrix.Basis
import Mathlib.Analysis.Norm... |
Analysis\Normed\Lp\ProdLp.lean | /-
Copyright (c) 2023 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll, Sébastien Gouëzel, Jireh Loreaux
-/
import Mathlib.Analysis.MeanInequalities
import Mathlib.Analysis.Normed.Lp.WithLp
/-!
# `L^p` distance on products of two metric spaces
... |
Analysis\Normed\Lp\WithLp.lean | /-
Copyright (c) 2023 Eric Wieser. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Eric Wieser
-/
import Mathlib.Data.ENNReal.Basic
import Mathlib.RingTheory.Finiteness
/-! # The `WithLp` type synonym
`WithLp p V` is a copy of `V` with exactly the same vector space st... |
Analysis\Normed\Module\Basic.lean | /-
Copyright (c) 2018 Patrick Massot. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Patrick Massot, Johannes Hölzl
-/
import Mathlib.Algebra.Algebra.Pi
import Mathlib.Algebra.Algebra.Prod
import Mathlib.Algebra.Algebra.Rat
import Mathlib.Algebra.Algebra.RestrictScalar... |
Analysis\Normed\Module\Complemented.lean | /-
Copyright (c) 2020 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov
-/
import Mathlib.Analysis.Normed.Operator.Banach
import Mathlib.Topology.Algebra.Module.FiniteDimension
/-!
# Complemented subspaces of normed vector spaces
A submo... |
Analysis\Normed\Module\Completion.lean | /-
Copyright (c) 2022 Yury G. Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury G. Kudryashov
-/
import Mathlib.Analysis.Normed.Group.Completion
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.Topology.Algebra.UniformRing
/-!
... |
Analysis\Normed\Module\Dual.lean | /-
Copyright (c) 2020 Heather Macbeth. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Heather Macbeth
-/
import Mathlib.Analysis.NormedSpace.HahnBanach.Extension
import Mathlib.Analysis.NormedSpace.RCLike
import Mathlib.Analysis.LocallyConvex.Polar
/-!
# The topologic... |
Analysis\Normed\Module\FiniteDimension.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Analysis.Asymptotics.AsymptoticEquivalent
import Mathlib.Analysis.Normed.Group.Lemmas
import Mathlib.Analysis.NormedSpace.AddTorsor
import Mathli... |
Analysis\Normed\Module\Ray.lean | /-
Copyright (c) 2022 Yury Kudryashov. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Yury Kudryashov, Yaël Dillies
-/
import Mathlib.LinearAlgebra.Ray
import Mathlib.Analysis.NormedSpace.Real
/-!
# Rays in a real normed vector space
In this file we prove some lemmas... |
Analysis\Normed\Module\Span.lean | /-
Copyright (c) 2024 Moritz Doll. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Moritz Doll
-/
import Mathlib.Analysis.Normed.Operator.LinearIsometry
import Mathlib.Analysis.Normed.Operator.ContinuousLinearMap
import Mathlib.Analysis.Normed.Module.Basic
/-!
# The s... |
Analysis\Normed\Module\WeakDual.lean | /-
Copyright (c) 2021 Kalle Kytölä. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Kalle Kytölä, Yury Kudryashov
-/
import Mathlib.Analysis.Normed.Module.Dual
import Mathlib.Analysis.NormedSpace.OperatorNorm.Completeness
/-!
# Weak dual of normed space
Let `E` be a n... |
Analysis\Normed\Operator\Banach.lean | /-
Copyright (c) 2019 Sébastien Gouëzel. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Sébastien Gouëzel
-/
import Mathlib.Topology.Baire.Lemmas
import Mathlib.Topology.Baire.CompleteMetrizable
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathli... |
Analysis\Normed\Operator\BanachSteinhaus.lean | /-
Copyright (c) 2021 Jireh Loreaux. All rights reserved.
Released under Apache 2.0 license as described in the file LICENSE.
Authors: Jireh Loreaux
-/
import Mathlib.Analysis.NormedSpace.OperatorNorm.NormedSpace
import Mathlib.Analysis.LocallyConvex.Barrelled
import Mathlib.Topology.Baire.CompleteMetrizable
/-!
# The... |
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