Theorems · Theorem · probability

ProbabilityTheory.Kernel.map_apply

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_4}
  {mγ : MeasurableSpace γ} {f : β → γ} (κ : ProbabilityTheory.Kernel α β),
  Measurable f → ∀ (a : α), (κ.map f) a = MeasureTheory.Measure.map f (κ a)

Defined in

Mathlib.Probability.Kernel.Composition.MapComap

Cited by

28 results in Mathlib

Foundations

Depth 204 from the axioms · uses propext, Classical.choice, Quot.sound