Theorems · Theorem · measure theory
MeasureTheory.Measure.AbsolutelyContinuous.mk
∀ {α : Type u_1} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α},
(∀ ⦃s : Set α⦄, MeasurableSet s → ν s = 0 → μ s = 0) → μ.AbsolutelyContinuous ν- Cited by
- 38 results in Mathlib
- Foundations
- Depth 175 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.Measure.AbsolutelyContinuousstatement · cited by 325
- MeasureTheory.measure_mono_nullproof · cited by 81
- MeasureTheory.exists_measurable_superset_of_nullproof · cited by 10
Cited by38
Results whose statement or proof uses this declaration.
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- MeasureTheory.Measure.quasiMeasurePreserving_sndproof · cited by 15
- MeasureTheory.Measure.quasiMeasurePreserving_fstproof · cited by 12
- MeasureTheory.Measure.AbsolutelyContinuous.mapproof · cited by 11
- MeasureTheory.quasiMeasurePreserving_invproof · cited by 7
- MeasureTheory.quasiMeasurePreserving_negproof · cited by 7
- MeasureTheory.Measure.AbsolutelyContinuous.compProd_leftproof · cited by 5
- MeasureTheory.absolutelyContinuous_invproof · cited by 5
- MeasureTheory.absolutelyContinuous_negproof · cited by 5
- MeasureTheory.withDensity_absolutelyContinuous'proof · cited by 5
- MeasureTheory.Measure.AbsolutelyContinuous.compProd_rightproof · cited by 4
- MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDerivproof · cited by 4