Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_eq_zero_of_mutuallySingular
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν ν' : MeasureTheory.Measure α} [μ.HaveLebesgueDecomposition ν']
[MeasureTheory.SigmaFinite ν'], μ.MutuallySingular ν → ν.AbsolutelyContinuous ν' → μ.rnDeriv ν' =ᵐ[ν] 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites35
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- Set.ofPredproof · cited by 6,101
- Filter.Eventuallyproof · cited by 3,134
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- Filter.univ_mem'proof · cited by 1,672
- MeasureTheory.Measure.restrictproof · cited by 1,646
Cited by5
Results whose statement or proof uses this declaration.
- MeasurableEmbedding.rnDeriv_mapproof · cited by 1
- MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingularproof · cited by 1
- MeasureTheory.Measure.rnDeriv_eq_zero_ae_singularPartproof · cited by 1
- ProbabilityTheory.rnDeriv_compProd_withDensity_rnDerivproof · cited by 1
- MeasureTheory.Measure.rnDeriv_mul_rnDeriv'proof · cited by 0