Theorems · Theorem · measure theory
MeasureTheory.Measure.MutuallySingular.symm
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ ν : MeasureTheory.Measure α}, ν.MutuallySingular μ → μ.MutuallySingular ν- Cited by
- 14 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.
Cites9
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
- compl_complproof · cited by 229
- MeasurableSet.complproof · cited by 172
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
Cited by14
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.MutuallySingular.zero_leftproof · cited by 8
- ProbabilityTheory.Kernel.mutuallySingular_singularPartproof · cited by 6
- MeasureTheory.Measure.MutuallySingular.compProd_of_rightproof · cited by 3
- MeasureTheory.Measure.MutuallySingular.commproof · cited by 2
- MeasureTheory.Measure.AbsolutelyContinuous.withDensity_rnDerivproof · cited by 2
- MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingularproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_rnDerivproof · cited by 1
- MeasureTheory.Measure.rnDeriv_eq_zero_ae_singularPartproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_rightproof · cited by 1
- MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iffproof · cited by 1
- MeasureTheory.MeasurePreserving.singularPartproof · cited by 1