Theorems · Theorem · measure theory
MeasureTheory.Measure.singularPart_eq_zero
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [μ.HaveLebesgueDecomposition ν],
μ.singularPart ν = 0 ↔ μ.AbsolutelyContinuous ν- Cited by
- 1 results in Mathlib
- Foundations
- Depth 213 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
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
- zero_addproof · cited by 2,366
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.withDensityproof · cited by 265
- MeasureTheory.Measure.rnDerivproof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.Measure.singularPartstatement and proof · cited by 71
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- MeasureTheory.Measure.haveLebesgueDecomposition_addproof · cited by 35
- MeasureTheory.Measure.singularPart_eq_zero_of_acproof · cited by 4
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.withDensity_rnDeriv_eqproof · cited by 31