Theorems · Theorem · measure theory

MeasureTheory.condExp_restrict_ae_eq_restrict

∀ {α : Type u_1} {E : Type u_2} {m m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [CompleteSpace E] {μ : MeasureTheory.Measure α} {f : α → E} {s : Set α} (hm : m ≤ m0)
  [MeasureTheory.SigmaFinite (μ.trim hm)],
  MeasurableSet s → MeasureTheory.Integrable f μ → (μ.restrict s)[f | m] =ᵐ[μ.restrict s] μ[f | m]

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator

Cited by

8 results in Mathlib

Foundations

Depth 301 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.SigmaFinite