Theorems · Theorem · measure theory

MeasureTheory.condExpIndSMul_ae_eq_smul

∀ {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) (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (x : G),
  ↑↑(MeasureTheory.condExpIndSMul hm hs hμs x) =ᵐ[μ] fun a =>
    ↑↑↑((MeasureTheory.condExpL2 ℝ ℝ hm) (MeasureTheory.indicatorConstLp 2 hs hμs 1)) a • x

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

4 results in Mathlib

Foundations

Depth 270 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

NormedAddCommGroupNormedSpace