Theorems · Theorem · measure theory

MeasureTheory.integral_condExpL2_eq_of_fin_meas_real

∀ {α : Type u_1} {𝕜 : Type u_7} [inst : RCLike 𝕜] {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s : Set α}
  {hm : m ≤ m0} (f : ↥(MeasureTheory.Lp 𝕜 2 μ)),
  MeasurableSet s → μ s ≠ ⊤ → ∫ (x : α) in s, ↑↑↑((MeasureTheory.condExpL2 𝕜 𝕜 hm) f) x ∂μ = ∫ (x : α) in s, ↑↑f x ∂μ

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

3 results in Mathlib

Foundations

Depth 271 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RCLike