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Theorems · Theorem · measure theory

MeasureTheory.condExp_indicator_aux

∀ {α : Type u_1} {E : Type u_2} {m m0 : MeasurableSpace α} [inst : NormedAddCommGroup E] [inst_1 : NormedSpace ℝ E]
  [CompleteSpace E] {μ : MeasureTheory.Measure α} {f : α → E} {s : Set α},
  MeasurableSet s → f =ᵐ[μ.restrict sᶜ] 0 → μ[s.indicator f | m] =ᵐ[μ] s.indicator μ[f | m]

Auxiliary lemma for condExp_indicator.

Defined in
Mathlib.MeasureTheory.Function.ConditionalExpectation.Indicator
Cited by
1 results in Mathlib
Foundations
Depth 299 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
NormedAddCommGroupNormedSpaceCompleteSpace

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