Theorems · Theorem · measure theory

MeasureTheory.condExp_of_sigmaFinite

∀ {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] (hm : m ≤ m₀) [hμm : MeasureTheory.SigmaFinite (μ.trim hm)],
  μ[f | m] =
    if MeasureTheory.Integrable f μ then
      if MeasureTheory.StronglyMeasurable f then f
      else MeasureTheory.AEStronglyMeasurable.mk ↑↑(MeasureTheory.condExpL1 hm μ f) ⋯
    else 0

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

5 results in Mathlib

Foundations

Depth 295 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite