Theorems · Theorem · measure theory
MeasureTheory.Measure.ae_le_iff_absolutelyContinuous
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α},
MeasureTheory.ae μ ≤ MeasureTheory.ae ν ↔ μ.AbsolutelyContinuous ν- Cited by
- 7 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- Filterstatement · cited by 8,121
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- Compl.complproof · cited by 2,925
- MeasureTheory.aestatement and proof · cited by 2,352
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.measure_eq_zero_iff_ae_notMemproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.AbsolutelyContinuous.ae_leproof · cited by 26
- Filter.EventuallyEq.restrictproof · cited by 3
- essSup_mono_measureproof · cited by 2
- MeasureTheory.absolutelyContinuous_toFiniteproof · cited by 2
- LE.le.absolutelyContinuous_of_aeproof · cited by 1
- MeasureTheory.toFinite_absolutelyContinuousproof · cited by 1
- essInf_antitone_measureproof · cited by 0