Theorems · Theorem · probability

ProbabilityTheory.Kernel.compProd_apply_eq_compProd_sectR

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_3}
  {mγ : MeasurableSpace γ} (κ : ProbabilityTheory.Kernel α β) (η : ProbabilityTheory.Kernel (α × β) γ)
  [ProbabilityTheory.IsSFiniteKernel κ] [ProbabilityTheory.IsSFiniteKernel η] (a : α),
  (κ.compProd η) a = (κ a).compProd (η.sectR a)

Defined in: Mathlib.Probability.Kernel.Composition.MeasureCompProd
Cited by: 0 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsSFiniteKernel ProbabilityTheory.IsSFiniteKernel

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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
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.SFiniteproof · cited by 449
MeasureTheory.Measure.extproof · cited by 308
ProbabilityTheory.IsSFiniteKernelstatement and proof · cited by 248
MeasureTheory.Measure.compProdstatement and proof · cited by 132

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