Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_withDensity_rnDeriv
∀ {α : Type u_1} {m : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [MeasureTheory.SigmaFinite μ]
[MeasureTheory.SigmaFinite ν], μ.AbsolutelyContinuous ν → μ.rnDeriv (μ.withDensity (ν.rnDeriv μ)) =ᵐ[μ] μ.rnDeriv ν- Cited by
- 1 results in Mathlib
- Foundations
- Depth 218 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites19
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.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- add_commproof · cited by 1,535
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- Filter.EventuallyEq.symmproof · cited by 408
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- MeasureTheory.Measure.withDensitystatement and proof · cited by 265
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- MeasureTheory.Measure.singularPartproof · cited by 71
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.inv_rnDerivproof · cited by 3