Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_eq_zero
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [μ.HaveLebesgueDecomposition ν],
μ.rnDeriv ν =ᵐ[ν] 0 ↔ μ.MutuallySingular ν- Cited by
- 6 results in Mathlib
- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- ENNRealstatement · cited by 9,879
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.MutuallySingularstatement · cited by 91
- MeasureTheory.Measure.measurable_rnDerivproof · cited by 75
- MeasureTheory.Measure.withDensity_rnDeriv_eq_zeroproof · cited by 3
- MeasureTheory.withDensity_eq_zero_iffproof · cited by 2
Cited by6
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_singularPartproof · cited by 2
- MeasureTheory.Measure.rnDeriv_zeroproof · cited by 2
- MeasureTheory.Measure.rnDeriv_add_of_mutuallySingularproof · cited by 2
- MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingularproof · cited by 1
- MeasureTheory.Measure.MutuallySingular.rnDeriv_ae_eq_zeroproof · cited by 0
- ProbabilityTheory.Kernel.rnDeriv_singularPartproof · cited by 0