Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_of_not_haveLebesgueDecomposition
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α},
¬μ.HaveLebesgueDecomposition ν → μ.rnDeriv ν = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 209 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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 and proof · cited by 9,879
- MeasureTheory.Measure.rnDerivstatement · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.rnDeriv_defproof · cited by 4
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.measurable_rnDerivproof · cited by 75
- MeasureTheory.pdf_of_not_haveLebesgueDecompositionproof · cited by 1
- MeasureTheory.Measure.MutuallySingular.rnDeriv_ae_eq_zeroproof · cited by 0