Theorems · Theorem · measure theory

MeasureTheory.condExpL2_indicator_of_measurable

∀ {α : Type u_1} {E : Type u_2} {𝕜 : Type u_7} [inst : RCLike 𝕜] [inst_1 : NormedAddCommGroup E]
  [inst_2 : InnerProductSpace 𝕜 E] [inst_3 : CompleteSpace E] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α}
  {s : Set α} (hm : m ≤ m0) (hs : MeasurableSet s) (hμs : μ s ≠ ⊤) (c : E),
  ↑((MeasureTheory.condExpL2 E 𝕜 hm) (MeasureTheory.indicatorConstLp 2 ⋯ hμs c)) =
    MeasureTheory.indicatorConstLp 2 ⋯ hμs c

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

3 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace