Theorems · Theorem · probability

MeasureTheory.Measure.comp_compProd_comm

∀ {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}
  {η : ProbabilityTheory.Kernel (α × β) γ} [MeasureTheory.SFinite μ] [ProbabilityTheory.IsSFiniteKernel η],
  (μ.compProd κ).bind ⇑η = (μ.bind ⇑(κ.compProd η)).snd

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

Mathlib docs Source Loogle LeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Cites29

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
Setproof · cited by 53,352
MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealproof · cited by 9,879
Set.preimageproof · cited by 4,946
MeasurableSetproof · cited by 3,075
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
MeasureTheory.lintegralproof · cited by 1,152
MeasureTheory.SFinitestatement and proof · cited by 449
MeasureTheory.Measure.extproof · cited by 308
ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248

Cited by1

Results whose statement or proof uses this declaration.

ProbabilityTheory.Kernel.HasSubgaussianMGF.integrable_exp_add_compProdproof · cited by 1