Theorems · Theorem · measure theory
MeasureTheory.Measure.withDensity_rnDeriv_eq_zero
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [μ.HaveLebesgueDecomposition ν],
ν.withDensity (μ.rnDeriv ν) = 0 ↔ μ.MutuallySingular ν- Cited by
- 3 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
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
- add_zeroproof · cited by 2,707
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
- MeasureTheory.Measure.singularPartproof · cited by 71
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- MeasureTheory.Measure.haveLebesgueDecomposition_addproof · cited by 35
- MeasureTheory.Measure.AbsolutelyContinuous.rflproof · cited by 30
- MeasureTheory.Measure.mutuallySingular_singularPartproof · cited by 27
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_eq_zeroproof · cited by 6
- MeasureTheory.Measure.singularPart_eq_selfproof · cited by 1
- MeasureTheory.Measure.mutuallySingular_compProd_left_iffproof · cited by 0