Theorems · Theorem · measure theory

MeasureTheory.Measure.bind_bind

∀ {α : Type u_1} {β : Type u_2} {mα : MeasurableSpace α} {mβ : MeasurableSpace β} {γ : Type u_3}
  [inst : MeasurableSpace γ] {m : MeasureTheory.Measure α} {f : α → MeasureTheory.Measure β}
  {g : β → MeasureTheory.Measure γ},
  AEMeasurable f m → AEMeasurable g (m.bind f) → (m.bind f).bind g = m.bind fun a => (f a).bind g

Defined in

Mathlib.MeasureTheory.Measure.GiryMonad

Cited by

2 results in Mathlib

Foundations

Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

MeasurableSpace