Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_eq_zero_ae_singularPart
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite μ]
[MeasureTheory.SigmaFinite ν], ∀ᵐ (x : α) ∂ν.singularPart μ, μ.rnDeriv ν x = 0- Cited by
- 1 results in Mathlib
- Foundations
- Depth 216 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
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 · cited by 9,879
- Filter.Eventuallystatement · cited by 3,134
- MeasureTheory.aestatement · cited by 2,352
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.Measure.rnDerivstatement · cited by 234
- MeasureTheory.Measure.singularPartstatement · cited by 71
- MeasureTheory.Measure.mutuallySingular_singularPartproof · cited by 27
- LE.le.absolutelyContinuousproof · cited by 20
- MeasureTheory.Measure.MutuallySingular.symmproof · cited by 14
- MeasureTheory.Measure.singularPart_leproof · cited by 7
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.ae_rnDeriv_ne_zero_imp_of_aeproof · cited by 1