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dd14c26 | 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 | import Mathlib
import OAI.Probability.LogConcave.JetEstimates.Bound
namespace OAI
section
section
noncomputable section
open MeasureTheory Filter
open scoped ENNReal NNReal Topology
section UpperProof
open MeasureTheory ProbabilityTheory Filter
open scoped ENNReal NNReal RealInnerProductSpace Topology
open Function MeasureTheory Set Filter
open scoped Topology NNReal
namespace LogConcaveSampling.JetCalculus
variable {E : Type*} [NormedAddCommGroup E] [NormedSpace ℝ E]
{ι κ : Type*}
lemma jet_map_positions (v : ι → E) (e : κ → ι) (l : List κ) (f : E → ℝ) :
jet v (l.map e) f=jet (v ∘ e) l f := by
induction l with
| nil => rfl
| cons i l ih => simp only [List.map_cons,jet,ih,Function.comp_apply]
lemma jet_finRange (v : ι → E) (l : List ι) (f : E → ℝ) :
jet v l f=jet (fun k : Fin l.length => v (l.get k)) (List.finRange l.length) f := by
change jet v l f=jet (v ∘ l.get) (List.finRange l.length) f
rw [← jet_map_positions]
congr 1
exact (List.map_get_finRange l).symm
end LogConcaveSampling.JetCalculus
end UpperProof
end
end
end
end OAI
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