Theorems · Theorem · measure theory
MeasureTheory.Measure.absolutelyContinuous_withDensity_rnDeriv_swap
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [ν.HaveLebesgueDecomposition μ],
(ν.withDensity (μ.rnDeriv ν)).AbsolutelyContinuous (μ.withDensity (ν.rnDeriv μ))- Cited by
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- Foundations
- Depth 212 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- MeasureTheory.Measure.AbsolutelyContinuousstatement · cited by 325
- MeasureTheory.Measure.withDensitystatement · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- MeasureTheory.withDensity_absolutelyContinuousproof · cited by 40
- MeasureTheory.Measure.absolutelyContinuous_of_leproof · cited by 14
- MeasureTheory.Measure.withDensity_rnDeriv_leproof · cited by 9
- MeasureTheory.Measure.AbsolutelyContinuous.withDensity_rnDerivproof · cited by 2
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