Theorems · Theorem · measure theory

MeasureTheory.inner_condExpL2_eq_inner_fun

∀ {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}
  (hm : m ≤ m0) (f g : ↥(MeasureTheory.Lp E 2 μ)),
  MeasureTheory.AEStronglyMeasurable (↑↑g) μ → inner 𝕜 (↑((MeasureTheory.condExpL2 E 𝕜 hm) f)) g = inner 𝕜 f g

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

0 results in Mathlib

Foundations

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

Assumes

RCLikeNormedAddCommGroupInnerProductSpaceCompleteSpace