Theorems · Theorem · probability

ProbabilityTheory.condDistrib_fst_prod

∀ {α : Type u_1} {β : Type u_2} {Ω : Type u_3} [inst : MeasurableSpace Ω] [inst_1 : StandardBorelSpace Ω]
  [inst_2 : Nonempty Ω] {mα : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  [inst_3 : MeasureTheory.IsFiniteMeasure μ] {Y : α → Ω} {mβ : MeasurableSpace β} {γ : Type u_5}
  {mγ : MeasurableSpace γ} (X : α → β),
  AEMeasurable Y μ →
    ∀ (ν : MeasureTheory.Measure γ) [inst_4 : MeasureTheory.IsProbabilityMeasure ν],
      ⇑(ProbabilityTheory.condDistrib (fun ω => Y ω.1) (fun ω => X ω.1) (μ.prod ν)) =ᵐ[MeasureTheory.Measure.map X μ]
        ⇑(ProbabilityTheory.condDistrib Y X μ)

Defined in

Mathlib.Probability.Kernel.CondDistrib

Cited by

0 results in Mathlib

Foundations

Depth 285 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasureMeasureTheory.IsProbabilityMeasure