Theorems · Theorem · probability

ProbabilityTheory.compProd_map_condDistrib

∀ {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] {X : α → β} {Y : α → Ω} {mβ : MeasurableSpace β},
  AEMeasurable Y μ →
    (MeasureTheory.Measure.map X μ).compProd (ProbabilityTheory.condDistrib Y X μ) =
      MeasureTheory.Measure.map (fun a => (X a, Y a)) μ

Defined in

Mathlib.Probability.Kernel.CondDistrib

Cited by

6 results in Mathlib

Foundations

Depth 280 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasure