Theorems · Theorem · measure theory
MeasureTheory.Measure.MutuallySingular.withDensity
∀ {α : Type u_1} {m0 : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} {f : α → ENNReal},
μ.MutuallySingular ν → (μ.withDensity f).MutuallySingular ν- Cited by
- 4 results in Mathlib
- Foundations
- Depth 205 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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.withDensitystatement · cited by 265
- MeasureTheory.Measure.MutuallySingularstatement and proof · cited by 91
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- MeasureTheory.Measure.AbsolutelyContinuous.rflproof · cited by 30
- MeasureTheory.Measure.MutuallySingular.mono_acproof · cited by 13
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_add_right_of_mutuallySingularproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_leftproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_withDensity_rnDeriv_rightproof · cited by 1
- MeasureTheory.Measure.rnDeriv_withDensity_rnDerivproof · cited by 1