Theorems · Theorem · probability

MeasureTheory.Measure.parallelComp_comp_compProd

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {μ : MeasureTheory.Measure α} {κ : ProbabilityTheory.Kernel α β}
  [ProbabilityTheory.IsSFiniteKernel κ] {η : ProbabilityTheory.Kernel β γ} [ProbabilityTheory.IsSFiniteKernel η],
  (μ.compProd κ).bind ⇑(ProbabilityTheory.Kernel.id.parallelComp η) = μ.compProd (η.comp κ)

Defined in: Mathlib.Probability.Kernel.Composition.Lemmas
Cited by: 1 results in Mathlib
Foundations: Depth 230 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsSFiniteKernel ProbabilityTheory.IsSFiniteKernel

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Cites18

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

DFunLike.coestatement and proof · cited by 62,936
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.SFiniteproof · cited by 449
ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
MeasureTheory.Measure.bindstatement and proof · cited by 173
MeasureTheory.Measure.compProdstatement and proof · cited by 132
ProbabilityTheory.Kernel.compstatement and proof · cited by 129
ProbabilityTheory.Kernel.idstatement and proof · cited by 72
ProbabilityTheory.Kernel.prodproof · cited by 65
ProbabilityTheory.Kernel.parallelCompstatement and proof · cited by 49

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.avgRisk_eq_lintegral_posterior_prodproof · cited by 1