Theorems · Theorem · probability

MeasureTheory.pdf.ae_lt_top

∀ {Ω : Type u_1} {E : Type u_2} [inst : MeasurableSpace E] {m : MeasurableSpace Ω} {ℙ : MeasureTheory.Measure Ω}
  [MeasureTheory.IsFiniteMeasure ℙ] {μ : MeasureTheory.Measure E} {X : Ω → E},
  ∀ᵐ (x : E) ∂μ, MeasureTheory.pdf X ℙ μ x < ⊤

Defined in: Mathlib.Probability.Density
Cited by: 1 results in Mathlib
Foundations: Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: MeasurableSpace MeasureTheory.IsFiniteMeasure

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Cites10

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

MeasurableSpacestatement and proof · cited by 13,106
MeasureTheory.Measurestatement and proof · cited by 10,939
ENNRealstatement · cited by 9,879
Top.topstatement · cited by 9,680
Filter.Eventuallystatement · cited by 3,134
MeasureTheory.aestatement · cited by 2,352
MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
MeasureTheory.Measure.mapproof · cited by 858
MeasureTheory.pdfstatement · cited by 32
MeasureTheory.Measure.rnDeriv_lt_topproof · cited by 21

Cited by1

Results whose statement or proof uses this declaration.

MeasureTheory.pdf.ofReal_toReal_ae_eqproof · cited by 1