Theorems · Theorem · probability

ProbabilityTheory.Kernel.ae_null_of_compProd_null

∀ {α : Type u_1} {β : Type u_2} {γ : Type u_3} {mα : MeasurableSpace α} {mβ : MeasurableSpace β}
  {mγ : MeasurableSpace γ} {s : Set (β × γ)} {κ : ProbabilityTheory.Kernel α β} [ProbabilityTheory.IsSFiniteKernel κ]
  {η : ProbabilityTheory.Kernel (α × β) γ} [ProbabilityTheory.IsSFiniteKernel η] {a : α},
  ((κ.compProd η) a) s = 0 → (fun b => (η (a, b)) (Prod.mk b ⁻¹' s)) =ᵐ[κ a] 0

Defined in: Mathlib.Probability.Kernel.Composition.CompProd
Cited by: 1 results in Mathlib
Foundations: Depth 228 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: ProbabilityTheory.IsSFiniteKernel ProbabilityTheory.IsSFiniteKernel

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Cites20

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

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Set.preimagestatement · cited by 4,946
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Filter.EventuallyEqstatement · cited by 1,912
ProbabilityTheory.Kernelstatement and proof · cited by 1,281
Filter.Eventually.of_forallproof · cited by 526
zero_leproof · cited by 382

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ProbabilityTheory.Kernel.ae_ae_of_ae_compProdproof · cited by 7