Theorems · Theorem · measure theory

MeasureTheory.integral_condExp

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

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

5 results in Mathlib

Foundations

Depth 298 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.SigmaFinite