Theorems · Theorem · measure theory

MeasureTheory.condExp_ae_eq_condExpL1

∀ {α : Type u_1} {E : Type u_3} {m m₀ : MeasurableSpace α} {μ : MeasureTheory.Measure α} [inst : NormedAddCommGroup E]
  [inst_1 : NormedSpace ℝ E] [CompleteSpace E] (hm : m ≤ m₀) [hμm : MeasureTheory.SigmaFinite (μ.trim hm)] (f : α → E),
  μ[f | m] =ᵐ[μ] ↑↑(MeasureTheory.condExpL1 hm μ f)

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

9 results in Mathlib

Foundations

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

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.SigmaFinite