path
stringlengths
11
71
content
stringlengths
75
124k
Order\SuccPred\IntervalSucc.lean
/- Copyright (c) 2022 Yury Kudryashov. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yury Kudryashov -/ import Mathlib.Data.Set.Pairwise.Basic import Mathlib.Data.Set.Lattice import Mathlib.Order.SuccPred.Basic /-! # Intervals `Ixx (f x) (f (Order.succ x))` In this ...
Order\SuccPred\Limit.lean
/- Copyright (c) 2022 Violeta Hernández Palacios. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Violeta Hernández Palacios -/ import Mathlib.Order.SuccPred.Basic import Mathlib.Order.BoundedOrder /-! # Successor and predecessor limits We define the predicate `Order....
Order\SuccPred\LinearLocallyFinite.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Data.Countable.Basic import Mathlib.Logic.Encodable.Basic import Mathlib.Order.SuccPred.Basic import Mathlib.Order.Interval.Finset.Defs import Mathlib.Alge...
Order\SuccPred\Relation.lean
/- Copyright (c) 2022 Floris van Doorn. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Floris van Doorn -/ import Mathlib.Order.SuccPred.Basic /-! # Relations on types with a `SuccOrder` This file contains properties about relations on types with a `SuccOrder` and th...
Order\UpperLower\Basic.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Sara Rousta -/ import Mathlib.Data.SetLike.Basic import Mathlib.Order.Interval.Set.OrdConnected import Mathlib.Order.Interval.Set.OrderIso import Mathlib.Data....
Order\UpperLower\Hom.lean
/- Copyright (c) 2022 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.UpperLower.Basic import Mathlib.Order.Hom.CompleteLattice /-! # `UpperSet.Ici` etc as `Sup`/`sSup`/`Inf`/`sInf`-homomorphisms In this ...
Order\UpperLower\LocallyFinite.lean
/- Copyright (c) 2023 Yaël Dillies, Sara Rousta. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies -/ import Mathlib.Order.Interval.Finset.Defs import Mathlib.Order.UpperLower.Basic /-! # Upper and lower sets in a locally finite order In this file we charac...
Probability\BorelCantelli.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Probability.Martingale.BorelCantelli import Mathlib.Probability.ConditionalExpectation import Mathlib.Probability.Independence.Basic /-! # The second Borel...
Probability\CDF.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.CondCDF /-! # Cumulative distribution function of a real probability measure The cumulative distribution function (cdf)...
Probability\CondCount.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Bhavik Mehta -/ import Mathlib.Probability.ConditionalProbability import Mathlib.MeasureTheory.Measure.Count /-! # Classical probability The classical formulation of probab...
Probability\ConditionalExpectation.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Probability.Notation import Mathlib.Probability.Independence.Basic import Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic /-! # Probabilistic p...
Probability\ConditionalProbability.lean
/- Copyright (c) 2022 Rishikesh Vaishnav. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rishikesh Vaishnav -/ import Mathlib.MeasureTheory.Measure.Typeclasses /-! # Conditional Probability This file defines conditional probability and includes basic results relating...
Probability\Density.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.Decomposition.RadonNikodym import Mathlib.MeasureTheory.Measure.Haar.OfBasis import Mathlib.Probability.Independence.Basic /-! # Probability d...
Probability\IdentDistrib.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Probability.Variance import Mathlib.MeasureTheory.Function.UniformIntegrable /-! # Identically distributed random variables Two random variable...
Probability\Integration.lean
/- Copyright (c) 2021 Martin Zinkevich. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Martin Zinkevich, Vincent Beffara -/ import Mathlib.MeasureTheory.Integral.SetIntegral import Mathlib.Probability.Independence.Basic /-! # Integration in Probability Theory Integra...
Probability\Moments.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Variance /-! # Moments and moment generating function ## Main definitions * `ProbabilityTheory.moment X p μ`: `p`th moment of a real random ...
Probability\Notation.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic import Mathlib.MeasureTheory.Decomposition.Lebesgue /-! # Notations for probability theory This file ...
Probability\StrongLaw.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel -/ import Mathlib.Probability.IdentDistrib import Mathlib.MeasureTheory.Integral.DominatedConvergence import Mathlib.Analysis.SpecificLimits.FloorPow import Mathli...
Probability\Variance.lean
/- Copyright (c) 2022 Sébastien Gouëzel. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Sébastien Gouëzel, Kexing Ying -/ import Mathlib.Probability.Notation import Mathlib.Probability.Integration import Mathlib.MeasureTheory.Function.L2Space /-! # Variance of random ...
Probability\Distributions\Exponential.lean
/- Copyright (c) 2023 Claus Clausen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Claus Clausen, Patrick Massot -/ import Mathlib.Probability.Notation import Mathlib.Probability.CDF import Mathlib.Probability.Distributions.Gamma /-! # Exponential distributions over ...
Probability\Distributions\Gamma.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Probability.Notation import Mathlib.Probability.CDF import Mathlib.Analysis.SpecialFunctions.Gamma.Basic /-! # Gamma distributions over ℝ Define the gamm...
Probability\Distributions\Gaussian.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Lorenzo Luccioli, Rémy Degenne, Alexander Bentkamp -/ import Mathlib.Analysis.SpecialFunctions.Gaussian.GaussianIntegral import Mathlib.Probability.Notation import Mathlib.MeasureTheory....
Probability\Distributions\Geometric.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Probability.ProbabilityMassFunction.Basic import Mathlib.MeasureTheory.Function.StronglyMeasurable.Basic /-! # Geometric distributions over ℕ Define the...
Probability\Distributions\Poisson.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker -/ import Mathlib.Analysis.SpecialFunctions.Exponential import Mathlib.Probability.ProbabilityMassFunction.Basic import Mathlib.MeasureTheory.Function.StronglyMeasurable.Ba...
Probability\Distributions\Uniform.lean
/- Copyright (c) 2024 Josha Dekker. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Josha Dekker, Devon Tuma, Kexing Ying -/ import Mathlib.Probability.Notation import Mathlib.Probability.Density import Mathlib.Probability.ConditionalProbability import Mathlib.Probabili...
Probability\Independence\Basic.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Independence.Kernel /-! # Independence of sets of sets and measure spaces (σ-algebras) * A family of sets of sets `π : ι → Set (Set Ω)` is in...
Probability\Independence\Conditional.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Independence.Kernel import Mathlib.Probability.Kernel.Condexp /-! # Conditional Independence We define conditional independence of sets/σ-alg...
Probability\Independence\Kernel.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Constructions.Pi import Mathlib.Probability.Kernel.Basic /-! # Independence with respect to a kernel and a measure A family of sets of sets...
Probability\Independence\ZeroOne.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Independence.Basic import Mathlib.Probability.Independence.Conditional /-! # Kolmogorov's 0-1 law Let `s : ι → MeasurableSpace Ω` be an indep...
Probability\Kernel\Basic.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Integral.Bochner import Mathlib.MeasureTheory.Measure.GiryMonad /-! # Markov Kernels A kernel from a measurable space `α` to another measur...
Probability\Kernel\Composition.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.MeasurableIntegral /-! # Product and composition of kernels We define * the composition-product `κ ⊗ₖ η` of two s-finite kernels `κ : ...
Probability\Kernel\CondDistrib.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.Unique import Mathlib.Probability.Notation /-! # Regular conditional probability distribution We define the regular con...
Probability\Kernel\Condexp.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.CondDistrib /-! # Kernel associated with a conditional expectation We define `condexpKernel μ m`, a kernel from `Ω` to `Ω` such that f...
Probability\Kernel\IntegralCompProd.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Composition import Mathlib.MeasureTheory.Integral.SetIntegral /-! # Bochner integral of a function against the composition-product of t...
Probability\Kernel\Invariance.lean
/- Copyright (c) 2023 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Probability.Kernel.Composition /-! # Invariance of measures along a kernel We say that a measure `μ` is invariant with respect to a kernel `κ` if its push-...
Probability\Kernel\MeasurableIntegral.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Basic import Mathlib.MeasureTheory.Constructions.Prod.Basic import Mathlib.MeasureTheory.Integral.DominatedConvergence /-! # Measurabil...
Probability\Kernel\MeasureCompProd.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.IntegralCompProd /-! # Composition-Product of a measure and a kernel This operation, denoted by `⊗ₘ`, takes `μ : Measure α` and `κ : K...
Probability\Kernel\RadonNikodym.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.Density import Mathlib.Probability.Kernel.WithDensity /-! # Radon-Nikodym derivative and Lebesgue decomposition for kern...
Probability\Kernel\WithDensity.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.MeasurableIntegral import Mathlib.MeasureTheory.Integral.SetIntegral /-! # With Density For an s-finite kernel `κ : Kernel α β` and a ...
Probability\Kernel\Disintegration\Basic.lean
/- Copyright (c) 2024 Yaël Dillies, Kin Yau James Wong. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Yaël Dillies, Kin Yau James Wong, Rémy Degenne -/ import Mathlib.Probability.Kernel.MeasureCompProd /-! # Disintegration of measures and kernels This file defines p...
Probability\Kernel\Disintegration\CDFToKernel.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Function.AEEqOfIntegral import Mathlib.Probability.Kernel.Composition import Mathlib.Probability.Kernel.Disintegration.MeasurableStieltjes /...
Probability\Kernel\Disintegration\CondCDF.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.Decomposition.RadonNikodym import Mathlib.Probability.Kernel.Disintegration.CDFToKernel /-! # Conditional cumulative distribution function ...
Probability\Kernel\Disintegration\Density.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Composition import Mathlib.Probability.Martingale.Convergence import Mathlib.Probability.Process.PartitionFiltration /-! # Kernel densi...
Probability\Kernel\Disintegration\Integral.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.StandardBorel /-! # Lebesgue and Bochner integrals of conditional kernels Integrals of `ProbabilityTheory.Kernel.condKe...
Probability\Kernel\Disintegration\MeasurableStieltjes.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Data.Complex.Abs import Mathlib.MeasureTheory.Measure.GiryMonad import Mathlib.MeasureTheory.Measure.Stieltjes import Mathlib.Analysis.Normed.Order.Lattice...
Probability\Kernel\Disintegration\StandardBorel.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Kernel.MeasureCompProd import Mathlib.Probability.Kernel.Disintegration.Basic import Mathlib.Probability.Kernel.Disintegration.CondCDF import M...
Probability\Kernel\Disintegration\Unique.lean
/- Copyright (c) 2023 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.Probability.Kernel.Disintegration.Integral /-! # Uniqueness of the conditional kernel We prove that the conditional kernels `ProbabilityTheor...
Probability\Martingale\Basic.lean
/- Copyright (c) 2021 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne, Kexing Ying -/ import Mathlib.Probability.Notation import Mathlib.Probability.Process.Stopping /-! # Martingales A family of functions `f : ι → Ω → E` is a martingale wit...
Probability\Martingale\BorelCantelli.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Probability.Martingale.Convergence import Mathlib.Probability.Martingale.OptionalStopping import Mathlib.Probability.Martingale.Centering /-! # Generalized...
Probability\Martingale\Centering.lean
/- Copyright (c) 2022 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Probability.Martingale.Basic /-! # Centering lemma for stochastic processes Any `ℕ`-indexed stochastic process which is adapted and integrable can be wri...
Probability\Martingale\Convergence.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.MeasureTheory.Constructions.Polish.Basic import Mathlib.MeasureTheory.Function.UniformIntegrable import Mathlib.Probability.Martingale.Upcrossing /-! # Mar...
Probability\Martingale\OptionalSampling.lean
/- Copyright (c) 2023 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.Order.SuccPred.LinearLocallyFinite import Mathlib.Probability.Martingale.Basic /-! # Optional sampling theorem If `τ` is a bounded stopping time and `σ` ...
Probability\Martingale\OptionalStopping.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Probability.Process.HittingTime import Mathlib.Probability.Martingale.Basic /-! # Optional stopping theorem (fair game theorem) The optional stopping theor...
Probability\Martingale\Upcrossing.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying -/ import Mathlib.Order.Interval.Set.Monotone import Mathlib.Probability.Process.HittingTime import Mathlib.Probability.Martingale.Basic import Mathlib.Tactic.AdaptationNote ...
Probability\ProbabilityMassFunction\Basic.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Devon Tuma -/ import Mathlib.Topology.Instances.ENNReal import Mathlib.MeasureTheory.Measure.Dirac /-! # Probability mass functions This file is about probability mas...
Probability\ProbabilityMassFunction\Binomial.lean
/- Copyright (c) 2023 Joachim Breitner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner -/ import Mathlib.Probability.ProbabilityMassFunction.Constructions import Mathlib.Tactic.FinCases /-! # The binomial distribution This file defines the probabilit...
Probability\ProbabilityMassFunction\Constructions.lean
/- Copyright (c) 2017 Johannes Hölzl. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Devon Tuma -/ import Mathlib.Probability.ProbabilityMassFunction.Monad /-! # Specific Constructions of Probability Mass Functions This file gives a number of differen...
Probability\ProbabilityMassFunction\Integrals.lean
/- Copyright (c) 2023 Joachim Breitner. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Joachim Breitner -/ import Mathlib.Probability.ProbabilityMassFunction.Basic import Mathlib.Probability.ProbabilityMassFunction.Constructions import Mathlib.MeasureTheory.Integral.Bo...
Probability\ProbabilityMassFunction\Monad.lean
/- Copyright (c) 2020 Devon Tuma. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johannes Hölzl, Devon Tuma -/ import Mathlib.Probability.ProbabilityMassFunction.Basic /-! # Monad Operations for Probability Mass Functions This file constructs two operations on `PMF` ...
Probability\Process\Adapted.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.Probability.Process.Filtration import Mathlib.Topology.Instances.Discrete /-! # Adapted and progressively measurable processes This file defi...
Probability\Process\Filtration.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.MeasureTheory.Function.ConditionalExpectation.Real /-! # Filtrations This file defines filtrations of a measurable space and σ-finite filtrat...
Probability\Process\HittingTime.lean
/- Copyright (c) 2022 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.Probability.Process.Stopping import Mathlib.Tactic.AdaptationNote /-! # Hitting time Given a stochastic process, the hitting time provides th...
Probability\Process\PartitionFiltration.lean
/- Copyright (c) 2024 Rémy Degenne. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Rémy Degenne -/ import Mathlib.MeasureTheory.MeasurableSpace.CountablyGenerated import Mathlib.Probability.Process.Filtration /-! # Filtration built from the finite partitions of a coun...
Probability\Process\Stopping.lean
/- Copyright (c) 2021 Kexing Ying. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kexing Ying, Rémy Degenne -/ import Mathlib.Probability.Process.Adapted import Mathlib.MeasureTheory.Constructions.BorelSpace.Order /-! # Stopping times, stopped processes and stopped va...
RepresentationTheory\Basic.lean
/- Copyright (c) 2022 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.Algebra.Group.Equiv.TypeTags import Mathlib.Algebra.Module.Defs import Mathlib.Algebra.MonoidAlgebra.Basic import Mathlib.LinearAlgebra.Dual import M...
RepresentationTheory\Character.lean
/- Copyright (c) 2022 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.RepresentationTheory.FDRep import Mathlib.LinearAlgebra.Trace import Mathlib.RepresentationTheory.Invariants /-! # Characters of representations Th...
RepresentationTheory\FDRep.lean
/- Copyright (c) 2022 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.RepresentationTheory.Rep import Mathlib.Algebra.Category.FGModuleCat.Limits import Mathlib.CategoryTheory.Preadditive.Schur import Mathlib.Representati...
RepresentationTheory\Invariants.lean
/- Copyright (c) 2022 Antoine Labelle. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Antoine Labelle -/ import Mathlib.RepresentationTheory.Basic import Mathlib.RepresentationTheory.FDRep /-! # Subspace of invariants a group representation This file introduces the s...
RepresentationTheory\Maschke.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.Algebra.MonoidAlgebra.Basic import Mathlib.LinearAlgebra.Basis.VectorSpace import Mathlib.RingTheory.SimpleModule /-! # Maschke's theorem We prove **...
RepresentationTheory\Rep.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.Algebra.Category.ModuleCat.Adjunctions import Mathlib.Algebra.Category.ModuleCat.Limits import Mathlib.Algebra.Category.ModuleCat.Colimits import Mathl...
RepresentationTheory\Action\Basic.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.Algebra.Category.Grp.Basic import Mathlib.CategoryTheory.SingleObj import Mathlib.CategoryTheory.Limits.FunctorCategory import Mathlib.CategoryTheory.L...
RepresentationTheory\Action\Concrete.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.Algebra.Group.Action.Pi import Mathlib.CategoryTheory.FintypeCat import Mathlib.RepresentationTheory.Action.Basic /-! # Constructors for `Action V G` ...
RepresentationTheory\Action\Continuous.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.RepresentationTheory.Action.Basic import Mathlib.Topology.Algebra.MulAction import Mathlib.Topology.Category.TopCat.Basic /-! # Topological subca...
RepresentationTheory\Action\Limits.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.CategoryTheory.Abelian.FunctorCategory import Mathlib.CategoryTheory.Abelian.Transfer import Mathlib.CategoryTheory.Linear.LinearFunctor import Mathlib...
RepresentationTheory\Action\Monoidal.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.RepresentationTheory.Action.Limits import Mathlib.RepresentationTheory.Action.Concrete import Mathlib.CategoryTheory.Monoidal.FunctorCategory import Ma...
RepresentationTheory\GroupCohomology\Basic.lean
/- Copyright (c) 2023 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Homology.Opposite import Mathlib.Algebra.Homology.ShortComplex.HomologicalComplex import Mathlib.RepresentationTheory.GroupCohomology.Res...
RepresentationTheory\GroupCohomology\Hilbert90.lean
/- Copyright (c) 2023 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.FieldTheory.Fixed import Mathlib.RepresentationTheory.GroupCohomology.LowDegree import Mathlib.LinearAlgebra.LinearIndependent /-! # Hilbert's T...
RepresentationTheory\GroupCohomology\LowDegree.lean
/- Copyright (c) 2023 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston, Joël Riou -/ import Mathlib.Algebra.Homology.ShortComplex.ModuleCat import Mathlib.RepresentationTheory.GroupCohomology.Basic import Mathlib.RepresentationTheory...
RepresentationTheory\GroupCohomology\Resolution.lean
/- Copyright (c) 2022 Amelia Livingston. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Amelia Livingston -/ import Mathlib.Algebra.Category.ModuleCat.Projective import Mathlib.AlgebraicTopology.ExtraDegeneracy import Mathlib.CategoryTheory.Abelian.Ext import Mathlib.R...
RingTheory\AdjoinRoot.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Chris Hughes -/ import Mathlib.Algebra.Algebra.Defs import Mathlib.Algebra.Polynomial.FieldDivision import Mathlib.FieldTheory.Minpoly.Basic import Mathlib.RingTheory.A...
RingTheory\Algebraic.lean
/- Copyright (c) 2019 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.RingTheory.IntegralClosure.IsIntegralClosure.Basic import Mathlib.RingTheory.Polynomial.IntegralNormalization /-! # Algebraic elements and algebraic e...
RingTheory\AlgebraicIndependent.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Algebra.MvPolynomial.Equiv import Mathlib.Algebra.MvPolynomial.Supported import Mathlib.LinearAlgebra.LinearIndependent import Mathlib.RingTheory.Adjoin.Ba...
RingTheory\AlgebraTower.lean
/- Copyright (c) 2020 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau -/ import Mathlib.Algebra.Algebra.Tower import Mathlib.Algebra.Module.BigOperators import Mathlib.LinearAlgebra.Basis /-! # Towers of algebras We set up the basic theory of alge...
RingTheory\Artinian.lean
/- Copyright (c) 2021 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.SetLike.Fintype import Mathlib.Algebra.Divisibility.Prod import Mathlib.RingTheory.Nakayama import Mathlib.RingTheory.SimpleModule import Mathlib.Tact...
RingTheory\Bezout.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.PrincipalIdealDomain /-! # Bézout rings A Bézout ring (Bezout ring) is a ring whose finitely generated ideals are principal. Notable examples i...
RingTheory\Binomial.lean
/- Copyright (c) 2023 Scott Carnahan. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Carnahan -/ import Mathlib.Algebra.Polynomial.Smeval import Mathlib.Algebra.Order.Floor import Mathlib.GroupTheory.GroupAction.Ring import Mathlib.RingTheory.Polynomial.Pochhamme...
RingTheory\ChainOfDivisors.lean
/- Copyright (c) 2021 Paul Lezeau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen, Paul Lezeau -/ import Mathlib.Algebra.IsPrimePow import Mathlib.Algebra.Squarefree.Basic import Mathlib.Order.Hom.Bounded import Mathlib.Algebra.GCDMonoid.Basic /-! # Chains...
RingTheory\ClassGroup.lean
/- Copyright (c) 2021 Anne Baanen. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Anne Baanen -/ import Mathlib.GroupTheory.QuotientGroup import Mathlib.RingTheory.DedekindDomain.Ideal /-! # The ideal class group This file defines the ideal class group `ClassGroup R`...
RingTheory\Complex.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.Complex.Module import Mathlib.RingTheory.Norm.Defs import Mathlib.RingTheory.Trace.Defs /-! # Lemmas about `Algebra.trace` and `Algebra.norm` on `ℂ` -/...
RingTheory\Discriminant.lean
/- Copyright (c) 2021 Riccardo Brasca. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Riccardo Brasca -/ import Mathlib.RingTheory.IntegralClosure.IntegrallyClosed import Mathlib.RingTheory.Trace.Basic import Mathlib.RingTheory.Norm.Basic /-! # Discriminant of a famil...
RingTheory\EisensteinCriterion.lean
/- Copyright (c) 2020 Chris Hughes. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Chris Hughes -/ import Mathlib.Data.Nat.Cast.WithTop import Mathlib.RingTheory.Prime import Mathlib.RingTheory.Polynomial.Content import Mathlib.RingTheory.Ideal.Quotient /-! # Eisenste...
RingTheory\EssentialFiniteness.lean
/- Copyright (c) 2024 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.RingTheory.FiniteType import Mathlib.RingTheory.TensorProduct.Basic /-! # Essentially of finite type algebras ## Main results - `Algebra.EssFiniteType`: Th...
RingTheory\EuclideanDomain.lean
/- Copyright (c) 2018 Mario Carneiro. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Mario Carneiro, Chris Hughes -/ import Mathlib.Algebra.GCDMonoid.Basic import Mathlib.Algebra.EuclideanDomain.Basic import Mathlib.RingTheory.Ideal.Basic import Mathlib.RingTheory.Prin...
RingTheory\Filtration.lean
/- Copyright (c) 2022 Andrew Yang. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Andrew Yang -/ import Mathlib.Algebra.Polynomial.Module.Basic import Mathlib.Algebra.Ring.Idempotents import Mathlib.RingTheory.Noetherian import Mathlib.RingTheory.ReesAlgebra import Mat...
RingTheory\Finiteness.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.Algebra.Algebra.RestrictScalars import Mathlib.Algebra.Algebra.Subalgebra.Basic import Mathlib.LinearAlgebra.Quotient import Mathlib.LinearAlgebra.StdB...
RingTheory\FinitePresentation.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.RingTheory.FiniteType import Mathlib.RingTheory.MvPolynomial.Tower import Mathlib.RingTheory.Ideal.QuotientOperations /-! # Finiteness conditions in c...
RingTheory\FiniteStability.lean
/- Copyright (c) 2024 Christian Merten. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Christian Merten -/ import Mathlib.LinearAlgebra.TensorProduct.RightExactness import Mathlib.RingTheory.FinitePresentation import Mathlib.RingTheory.TensorProduct.MvPolynomial /-! ...
RingTheory\FiniteType.lean
/- Copyright (c) 2020 Johan Commelin. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Johan Commelin -/ import Mathlib.RingTheory.Adjoin.Tower /-! # Finiteness conditions in commutative algebra In this file we define a notion of finiteness that is common in commutativ...
RingTheory\Fintype.lean
/- Copyright (c) 2020 Scott Morrison. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Scott Morrison -/ import Mathlib.Data.Fintype.Units import Mathlib.Data.ZMod.Basic /-! # Some facts about finite rings -/ open Finset ZMod variable {R : Type*} [Ring R] [Fintype R]...
RingTheory\FreeCommRing.lean
/- Copyright (c) 2019 Kenny Lau. All rights reserved. Released under Apache 2.0 license as described in the file LICENSE. Authors: Kenny Lau, Johan Commelin -/ import Mathlib.Algebra.MvPolynomial.Equiv import Mathlib.Algebra.MvPolynomial.CommRing import Mathlib.Logic.Equiv.Functor import Mathlib.RingTheory.FreeRing /-...