Theorems · Theorem · measure theory

MeasureTheory.condExp_of_stronglyMeasurable

∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] (hm : m ≤ m₀) [hμm : MeasureTheory.SigmaFinite (μ.trim hm)] {f : α → E},
  MeasureTheory.StronglyMeasurable f → MeasureTheory.Integrable f μ → μ[f | m] = f

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

21 results in Mathlib

Foundations

Depth 296 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite