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Theorems · Theorem · measure theory

MeasureTheory.Measure.mutuallySingular_singularPart

∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α), (μ.singularPart ν).MutuallySingular ν
Defined in
Mathlib.MeasureTheory.Measure.Decomposition.Lebesgue
Cited by
27 results in Mathlib
Foundations
Depth 210 from the axioms · uses propext, Classical.choice, Quot.sound

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

MeasureTheory.Measure.singularPart_eq_zero_of_ac · cited by 4Measure.singularPart_eq_z…MeasureTheory.Measure.singularPart_smul · cited by 4Measure.singularPart_smulMeasureTheory.Measure.absolutelyContinuous_withDensity_rnDeriv · cited by 4Measure.absolutelyContinu…VitaliFamily.ae_tendsto_rnDeriv · cited by 4VitaliFamily.ae_tendsto_r…MeasureTheory.Measure.withDensity_rnDeriv_eq_zero · cited by 3Measure.withDensity_rnDer…MeasureTheory.Measure.singularPart_add · cited by 2Measure.singularPart_addMeasureTheory.Measure.AbsolutelyContinuous.withDensity_rnDeriv · cited by 2AbsolutelyContinuous.with…MeasureTheory.Measure.singularPart_smul_right · cited by 2Measure.singularPart_smul…MeasureTheory.Measure.rnDeriv_singularPart · cited by 2Measure.rnDeriv_singularP…MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingular · cited by 1Measure.rnDeriv_add_right…MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingular' · cited by 1Measure.rnDeriv_add_right…MeasureTheory.Measure.rnDeriv_eq_zero_ae_singularPart · cited by 1Measure.rnDeriv_eq_zero_a…MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iff · cited by 1AbsolutelyContinuous.mutu…MeasureTheory.MeasurePreserving.singularPart · cited by 1MeasurePreserving.singula…MeasureTheory.Measure.singularPart_eq_self · cited by 1Measure.singularPart_eq_s…MeasurableSpace · cited by 13106MeasurableSpaceMeasureTheory.Measure · cited by 10939MeasureTheory.MeasureMeasureTheory.Measure.HaveLebesgueDecomposition · cited by 92Measure.HaveLebesgueDecom…MeasureTheory.Measure.MutuallySingular · cited by 91Measure.MutuallySingularMeasureTheory.Measure.singularPart · cited by 71Measure.singularPartMeasureTheory.Measure.MutuallySingular.zero_left · cited by 8MutuallySingular.zero_leftMeasureTheory.Measure.haveLebesgueDecomposition_spec · cited by 6Measure.haveLebesgueDecom…MeasureTheory.Measure.singularPart_of_not_haveLebesgueDecomposition · cited by 1Measure.singularPart_of_n…Measure.mutuallySingular_sing…CITED BYCITES

Cites8

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Cited by27

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