Theorems · Theorem · measure theory
MeasureTheory.condExp_mul_of_stronglyMeasurable_left
∀ {Ω : Type u_1} {m mΩ : MeasurableSpace Ω} {μ : MeasureTheory.Measure Ω} {f g : Ω → ℝ},
MeasureTheory.StronglyMeasurable f →
MeasureTheory.Integrable (f * g) μ → MeasureTheory.Integrable g μ → μ[f * g | m] =ᵐ[μ] f * μ[g | m]Pull-out property of the conditional expectation.
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- Foundations
- Depth 305 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
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- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- MeasureTheory.Integrablestatement and proof · cited by 1,367
- MeasureTheory.StronglyMeasurablestatement and proof · cited by 363
- MeasureTheory.condExpstatement · cited by 234
- MeasureTheory.StronglyMeasurable.aestronglyMeasurableproof · cited by 94
- ContinuousLinearMap.mulproof · cited by 63
- MeasureTheory.condExp_bilin_of_aestronglyMeasurable_leftproof · cited by 5
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