Theorems · Theorem · measure theory

MeasureTheory.Measure.bind_apply

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {m : MeasureTheory.Measure α}
  {f : α → MeasureTheory.Measure β} {s : Set β},
  MeasurableSet s → AEMeasurable f m → (m.bind f) s = ∫⁻ (a : α), (f a) s ∂m

Defined in

Mathlib.MeasureTheory.Measure.GiryMonad

Cited by

21 results in Mathlib

Foundations

Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound