Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_restrict_self
∀ {α : Type u_1} {m : MeasurableSpace α} (ν : MeasureTheory.Measure α) [MeasureTheory.SigmaFinite ν] {s : Set α},
MeasurableSet s → (ν.restrict s).rnDeriv ν =ᵐ[ν] s.indicator 1The Radon-Nikodym derivative of the restriction of a measure to a measurable set is the indicator function of this set.
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- MeasureTheory.SigmaFinite
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites15
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement · cited by 9,879
- MeasurableSetstatement and proof · cited by 3,075
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.Measure.restrictstatement · cited by 1,646
- Set.indicatorstatement and proof · cited by 723
- MeasureTheory.SigmaFinitestatement and proof · cited by 526
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- Measurable.indicatorproof · cited by 38
Cited by1
Results whose statement or proof uses this declaration.
- VitaliFamily.ae_tendsto_measure_inter_div_of_measurableSetproof · cited by 2