Theorems · Definition · measure theory
MeasureTheory.Measure.AbsolutelyContinuous
{α : Type u_1} → {_m0 : MeasurableSpace α} → MeasureTheory.Measure α → MeasureTheory.Measure α → PropWe say that μ is absolutely continuous with respect to ν, or that μ is dominated by ν,
if ν(A) = 0 implies that μ(A) = 0.
- Cited by
- 325 results in Mathlib
- Foundations
- Depth 170 from the axioms, rests on 4,584 definitions · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
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
Cited by331
Results whose statement or proof uses this declaration.
- MeasureTheory.withDensity_absolutelyContinuousstatement · cited by 40
- MeasureTheory.Measure.AbsolutelyContinuous.mkstatement · cited by 38
- MeasureTheory.Measure.withDensity_rnDeriv_eqstatement and proof · cited by 31
- MeasureTheory.Measure.AbsolutelyContinuous.rflstatement · cited by 30
- MeasureTheory.Measure.AbsolutelyContinuous.ae_lestatement · cited by 26
- MeasureTheory.Measure.QuasiMeasurePreserving.compproof · cited by 21
- MeasureTheory.Measure.QuasiMeasurePreserving.absolutelyContinuousstatement · cited by 20
- LE.le.absolutelyContinuousstatement · cited by 20
- MeasureTheory.Measure.AbsolutelyContinuous.transstatement and proof · cited by 17
- MeasureTheory.Measure.absolutelyContinuous_of_lestatement · cited by 14
- MeasureTheory.AEStronglyMeasurable.mono_acstatement and proof · cited by 14
- MeasureTheory.Measure.MutuallySingular.mono_acstatement and proof · cited by 13
Showing the 200 most cited of 331.