Theorems · Theorem · measure theory
MeasureTheory.withDensity_absolutelyContinuous
∀ {α : Type u_1} {m : MeasurableSpace α} (μ : MeasureTheory.Measure α) (f : α → ENNReal),
(μ.withDensity f).AbsolutelyContinuous μ- Cited by
- 40 results in Mathlib
- Foundations
- Depth 204 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.
- DFunLike.coeproof · cited by 62,936
- 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
- MeasurableSetproof · cited by 3,075
- MeasureTheory.Measure.AbsolutelyContinuousstatement · cited by 325
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.withDensity_applyproof · cited by 73
- MeasureTheory.Measure.AbsolutelyContinuous.mkproof · cited by 38
- MeasureTheory.setLIntegral_measure_zeroproof · cited by 5
Cited by40
Results whose statement or proof uses this declaration.
- MeasureTheory.setLIntegral_condLExpproof · cited by 8
- MeasureTheory.Measure.eq_singularPartproof · cited by 6
- MeasureTheory.lintegral_withDensity_eq_lintegral_mul₀proof · cited by 6
- MeasureTheory.Measure.MutuallySingular.withDensityproof · cited by 4
- VitaliFamily.ae_tendsto_rnDerivproof · cited by 4
- MeasureTheory.Measure.withDensity_rnDeriv_eq_zeroproof · cited by 3
- MeasureTheory.Measure.inv_rnDerivproof · cited by 3
- MeasureTheory.tilted_absolutelyContinuousproof · cited by 2
- MeasureTheory.withDensity_apply_eq_zero'proof · cited by 2
- MeasureTheory.withDensity_apply₀proof · cited by 2
- ProbabilityTheory.rnDeriv_measure_compProd_leftproof · cited by 2
- MeasureTheory.Measure.rnDeriv_withDensity_leftproof · cited by 2