Theorems · Theorem · measure theory

MeasureTheory.condExp_ae_eq_condExpL1CLM

∀ {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] [inst_2 : CompleteSpace E] (hm : m ≤ m₀)
  [inst_3 : MeasureTheory.SigmaFinite (μ.trim hm)] (hf : MeasureTheory.Integrable f μ),
  μ[f | m] =ᵐ[μ] ↑↑((MeasureTheory.condExpL1CLM E hm μ) (MeasureTheory.Integrable.toL1 f hf))

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.Basic

Cited by

0 results in Mathlib

Foundations

Depth 297 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceCompleteSpaceMeasureTheory.SigmaFinite