Theorems · Theorem · measure theory

MeasureTheory.setIntegral_condExpL2_indicator

∀ {α : Type u_1} {m m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {s t : Set α} {hm : m ≤ m0},
  MeasurableSet s →
    ∀ (ht : MeasurableSet t),
      μ s ≠ ⊤ →
        ∀ (hμt : μ t ≠ ⊤),
          ∫ (x : α) in s, ↑↑↑((MeasureTheory.condExpL2 ℝ ℝ hm) (MeasureTheory.indicatorConstLp 2 ht hμt 1)) x ∂μ =
            μ.real (t ∩ s)

Defined in

Mathlib.MeasureTheory.Function.ConditionalExpectation.CondexpL2

Cited by

2 results in Mathlib

Foundations

Depth 274 from the axioms · uses propext, Classical.choice, Quot.sound