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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
Defined in
Mathlib.MeasureTheory.Measure.AbsolutelyContinuous
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.

MeasureTheory.withDensity_absolutelyContinuous · cited by 40MeasureTheory.withDensity…MeasureTheory.Measure.quasiMeasurePreserving_snd · cited by 15Measure.quasiMeasurePrese…MeasureTheory.Measure.quasiMeasurePreserving_fst · cited by 12Measure.quasiMeasurePrese…MeasureTheory.Measure.AbsolutelyContinuous.map · cited by 11AbsolutelyContinuous.mapMeasureTheory.quasiMeasurePreserving_inv · cited by 7MeasureTheory.quasiMeasur…MeasureTheory.quasiMeasurePreserving_neg · cited by 7MeasureTheory.quasiMeasur…MeasureTheory.Measure.AbsolutelyContinuous.compProd_left · cited by 5AbsolutelyContinuous.comp…MeasureTheory.absolutelyContinuous_inv · cited by 5MeasureTheory.absolutelyC…MeasureTheory.absolutelyContinuous_neg · cited by 5MeasureTheory.absolutelyC…MeasureTheory.withDensity_absolutelyContinuous' · cited by 5MeasureTheory.withDensity…MeasureTheory.Measure.AbsolutelyContinuous.compProd_right · cited by 4AbsolutelyContinuous.comp…MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDeriv · cited by 4Measure.absolutelyContinu…MeasureTheory.Measure.mconv_absolutelyContinuous · cited by 3Measure.mconv_absolutelyC…MeasureTheory.Measure.AbsolutelyContinuous.prod · cited by 3AbsolutelyContinuous.prodMeasureTheory.Measure.absolutelyContinuous_of_compProd · cited by 3Measure.absolutelyContinu…DFunLike.coe · cited by 62936DFunLike.coeSet · cited by 53352SetMeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureENNReal · cited by 9879ENNRealMeasurableSet · cited by 3075MeasurableSetMeasureTheory.Measure.AbsolutelyContinuous · cited by 325Measure.AbsolutelyContinu…MeasureTheory.measure_mono_null · cited by 81MeasureTheory.measure_mon…MeasureTheory.exists_measurable_superset_of_null · cited by 10MeasureTheory.exists_meas…AbsolutelyContinuous.mkCITED BYCITES

Cites9

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

Cited by38

Results whose statement or proof uses this declaration.