Theorems · Theorem · measure theory
MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDeriv
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [ν.HaveLebesgueDecomposition μ],
μ.AbsolutelyContinuous ν → μ.AbsolutelyContinuous (μ.withDensity (ν.rnDeriv μ))- Cited by
- 4 results in Mathlib
- Foundations
- Depth 211 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites21
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
- LE.le.transproof · cited by 3,151
- MeasurableSetproof · cited by 3,075
- Compl.complproof · cited by 2,925
- Set.inter_subset_leftproof · cited by 360
- Set.inter_subset_rightproof · cited by 329
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.inv_rnDerivproof · cited by 3
- MeasureTheory.Measure.rnDeriv_withDensity_rnDerivproof · cited by 1
- MeasureTheory.Measure.rnDeriv_pos'proof · cited by 1
- MeasureTheory.Measure.AbsolutelyContinuous.mutuallySingular_compProd_iffproof · cited by 1