Theorems · Theorem · measure theory

MeasureTheory.condExpInd_ae_eq_condExpIndSMul

∀ {α : Type u_1} {G : Type u_4} [inst : NormedAddCommGroup G] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {s : Set α} [inst_1 : NormedSpace ℝ G] (hm : m ≤ m0) [inst_2 : MeasureTheory.SigmaFinite (μ.trim hm)]
  (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (x : G),
  ↑↑((MeasureTheory.condExpInd G hm μ s) x) =ᵐ[μ] ↑↑(MeasureTheory.condExpIndSMul hm hs hμs x)

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL1

Cited by

5 results in Mathlib

Foundations

Depth 282 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpaceMeasureTheory.SigmaFinite