Theorems · Theorem · probability

ProbabilityTheory.condDistrib_map

∀ {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} {X : α → β} {Y : α → Ω} {mβ : MeasurableSpace β} {γ : Type u_5}
  {mγ : MeasurableSpace γ} {ν : MeasureTheory.Measure γ} [inst_3 : MeasureTheory.IsFiniteMeasure ν] {f : γ → α},
  AEMeasurable X (MeasureTheory.Measure.map f ν) →
    AEMeasurable Y (MeasureTheory.Measure.map f ν) →
      AEMeasurable f ν →
        ⇑(ProbabilityTheory.condDistrib Y X (MeasureTheory.Measure.map f ν)) =ᵐ[MeasureTheory.Measure.map (X ∘ f) ν]
          ⇑(ProbabilityTheory.condDistrib (Y ∘ f) (X ∘ f) ν)

Defined in

Mathlib.Probability.Kernel.CondDistrib

Cited by

2 results in Mathlib

Foundations

Depth 284 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasure