Theorems · Theorem · measure theory

MeasureTheory.integrable_condExpIndSMul

∀ {α : Type u_1} {G : Type u_5} [inst : NormedAddCommGroup G] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {s : Set α} [inst_1 : NormedSpace ℝ G] (hm : m ≤ m0) [MeasureTheory.SigmaFinite (μ.trim hm)] (hs : MeasurableSet s)
  (hμs : μ s ≠ ⊤) (x : G), MeasureTheory.Integrable (↑↑(MeasureTheory.condExpIndSMul hm hs hμs x)) μ

If the measure μ.trim hm is sigma-finite, then the conditional expectation of a measurable set with finite measure is integrable.

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

2 results in Mathlib

Foundations

Depth 275 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite