Theorems · Theorem · probability

ProbabilityTheory.condDistrib_congr

∀ {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} {X' : α → β} {Y' : α → Ω},
  Y =ᵐ[μ] Y' → X =ᵐ[μ] X' → ProbabilityTheory.condDistrib Y X μ = ProbabilityTheory.condDistrib Y' X' μ

Defined in

Mathlib.Probability.Kernel.CondDistrib

Cited by

3 results in Mathlib

Foundations

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

Assumes

MeasurableSpaceStandardBorelSpaceNonemptyMeasureTheory.IsFiniteMeasure