Theorems · Theorem · measure theory

MeasureTheory.lintegral_enorm_condExp_indicator

∀ {𝓧 : Type u_1} {m m𝓧 : MeasurableSpace 𝓧} (hm : m ≤ m𝓧) {μ : MeasureTheory.Measure 𝓧}
  [MeasureTheory.SigmaFinite (μ.trim hm)] {s : Set 𝓧},
  MeasurableSet s →
    autoParam (μ s ≠ ⊤) MeasureTheory.lintegral_enorm_condExp_indicator._auto_1 →
      ∫⁻ (a : 𝓧), ‖μ[s.indicator 1 | m] a‖ₑ ∂μ = μ s

Defined in: Mathlib.MeasureTheory.Function.ConditionalExpectation.LebesgueBochner
Cited by: 1 results in Mathlib
Foundations: Depth 302 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasureTheory.SigmaFinite

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

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Set.indicatorstatement and proof · cited by 723

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.VectorMeasure.exists_extension_of_isSetSemiring_of_le_measureproof · cited by 0