Theorems · Theorem · measure theory
MeasureTheory.Measure.eq_zero_of_absolutelyContinuous_of_mutuallySingular
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ ν : MeasureTheory.Measure α},
μ.AbsolutelyContinuous ν → μ.MutuallySingular ν → μ = 0- Cited by
- 2 results in Mathlib
- Foundations
- Depth 199 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
- MeasureTheory.Measure.AbsolutelyContinuous.rflproof · cited by 30
- MeasureTheory.Measure.MutuallySingular.mono_acproof · cited by 13
- MeasureTheory.Measure.MutuallySingular.self_iffproof · cited by 4
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.AbsolutelyContinuous.kernel_of_compProdproof · cited by 5
- ProbabilityTheory.Kernel.singularPart_eq_zero_iff_absolutelyContinuousproof · cited by 2