Theorems · Theorem · probability

ProbabilityTheory.condDistrib_comp

∀ {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} {Ω' : Type u_5}
  {mΩ' : MeasurableSpace Ω'} [inst_4 : StandardBorelSpace Ω'] [inst_5 : Nonempty Ω'] (X : α → β),
  AEMeasurable Y μ →
    ∀ {f : Ω → Ω'},
      Measurable f →
        ⇑(ProbabilityTheory.condDistrib (f ∘ Y) X μ) =ᵐ[MeasureTheory.Measure.map X μ]
          ⇑((ProbabilityTheory.condDistrib Y X μ).map f)

Defined in

Mathlib.Probability.Kernel.CondDistrib

Cited by

0 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasureStandardBorelSpaceNonempty