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- 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.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- MeasureTheory.Measure.HaveLebesgueDecompositionproof · cited by 92
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
- MeasureTheory.Measure.singularPartstatement · cited by 71
- MeasureTheory.Measure.MutuallySingular.zero_leftproof · cited by 8
- MeasureTheory.Measure.haveLebesgueDecomposition_specproof · cited by 6
- MeasureTheory.Measure.singularPart_of_not_haveLebesgueDecompositionproof · cited by 1
Cited by27
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.singularPart_eq_zero_of_acproof · cited by 4
- MeasureTheory.Measure.singularPart_smulproof · cited by 4
- MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDerivproof · cited by 4
- VitaliFamily.ae_tendsto_rnDerivproof · cited by 4
- MeasureTheory.Measure.withDensity_rnDeriv_eq_zeroproof · cited by 3
- MeasureTheory.Measure.singularPart_addproof · cited by 2
- MeasureTheory.Measure.AbsolutelyContinuous.withDensity_rnDerivproof · cited by 2
- MeasureTheory.Measure.singularPart_smul_rightproof · cited by 2
- MeasureTheory.Measure.rnDeriv_singularPartproof · cited by 2
- MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingularproof · cited by 1
- MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingular'proof · cited by 1
- MeasureTheory.Measure.rnDeriv_eq_zero_ae_singularPartproof · cited by 1