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Theorems · Theorem · probability

MeasureTheory.pdf.ofReal_toReal_ae_eq

∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {m : MeasurableSpace Ω} {ℙ : MeasureTheory.Measure Ω}
  {μ : MeasureTheory.Measure E} [MeasureTheory.IsFiniteMeasure ℙ] {X : Ω → E},
  (fun x => ENNReal.ofReal (MeasureTheory.pdf X ℙ μ x).toReal) =ᵐ[μ] MeasureTheory.pdf X ℙ μ
Defined in
Mathlib.Probability.Density
Cited by
1 results in Mathlib
Foundations
Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
MeasurableSpaceMeasureTheory.IsFiniteMeasure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.pdf.hasFiniteIntegral_mul · cited by 1pdf.hasFiniteIntegral_mulMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasureTheory.ae · cited by 2352MeasureTheory.aeFilter.EventuallyEq · cited by 1912Filter.EventuallyEqMeasureTheory.IsFiniteMeasure · cited by 1078MeasureTheory.IsFiniteMea…ENNReal.ofReal · cited by 863ENNReal.ofRealENNReal.toReal · cited by 859ENNReal.toRealMeasureTheory.pdf · cited by 32MeasureTheory.pdfMeasureTheory.ofReal_toReal_ae_eq · cited by 2MeasureTheory.ofReal_toRe…MeasureTheory.pdf.ae_lt_top · cited by 1pdf.ae_lt_toppdf.ofReal_toReal_ae_eqCITED BYCITES

Cites11

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Cited by1

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