Theorems · Theorem · measure theory
MeasureTheory.Measure.MutuallySingular.mono_ac
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ₁ μ₂ ν₁ ν₂ : MeasureTheory.Measure α},
μ₁.MutuallySingular ν₁ → μ₂.AbsolutelyContinuous μ₁ → ν₂.AbsolutelyContinuous ν₁ → μ₂.MutuallySingular ν₂- Cited by
- 13 results in Mathlib
- Foundations
- Depth 172 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.
- 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
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
Cited by13
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.MutuallySingular.withDensityproof · cited by 4
- MeasureTheory.Measure.singularPart_eq_zero_of_acproof · cited by 4
- MeasureTheory.Measure.MutuallySingular.monoproof · cited by 3
- MeasureTheory.Measure.withDensity_rnDeriv_eq_zeroproof · cited by 3
- MeasureTheory.Measure.MutuallySingular.smulproof · cited by 2
- MeasureTheory.Measure.AbsolutelyContinuous.withDensity_rnDerivproof · cited by 2
- MeasureTheory.Measure.singularPart_smul_rightproof · cited by 2
- MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iffproof · cited by 1
- MeasureTheory.Measure.MutuallySingular.congr_acproof · cited by 0