Theorems · Theorem · probability

ProbabilityTheory.Kernel.comapRight_compProd_id_prod

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {δ : Type u_4} {mδ : MeasurableSpace δ} (κ : ProbabilityTheory.Kernel α β)
  [ProbabilityTheory.IsSFiniteKernel κ] (η : ProbabilityTheory.Kernel (α × β) γ) [ProbabilityTheory.IsSFiniteKernel η]
  {f : δ → γ} (hf : MeasurableEmbedding f), (κ.compProd η).comapRight ⋯ = κ.compProd (η.comapRight hf)

Defined in: Mathlib.Probability.Kernel.Composition.CompProd
Cited by: 1 results in Mathlib
Foundations: Depth 227 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsSFiniteKernel ProbabilityTheory.IsSFiniteKernel

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DFunLike.coeproof · cited by 62,936
Setproof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measureproof · cited by 10,939
ENNRealproof · cited by 9,879
Set.imageproof · cited by 5,609
Set.preimageproof · cited by 4,946
MeasurableSetproof · cited by 3,075
Set.extproof · cited by 2,266
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.lintegralproof · cited by 1,152
DFunLikeproof · cited by 576

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ProbabilityTheory.Kernel.compProd_fst_borelMarkovFromReal_eq_comapRight_compProdproof · cited by 1