Theorems · Theorem · probability

ProbabilityTheory.condDistrib_comp_self

∀ {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] {mβ : MeasurableSpace β} (X : α → β) {f : β → Ω} (hf : Measurable f),
  ⇑(ProbabilityTheory.condDistrib (f ∘ X) X μ) =ᵐ[MeasureTheory.Measure.map X μ]
    ⇑(ProbabilityTheory.Kernel.deterministic f hf)

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