Theorems · Theorem · probability

ProbabilityTheory.integrable_toReal_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} {s : Set Ω},
  AEMeasurable X μ →
    MeasurableSet s → MeasureTheory.Integrable (fun a => ((ProbabilityTheory.condDistrib Y X μ) (X a)).real s) μ

Defined in

Mathlib.Probability.Kernel.CondDistrib

Cited by

2 results in Mathlib

Foundations

Depth 281 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasure