Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_smul_left
∀ {α : Type u_1} {m : MeasurableSpace α} (ν μ : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure ν]
[ν.HaveLebesgueDecomposition μ] (r : NNReal), (r • ν).rnDeriv μ =ᵐ[μ] r • ν.rnDeriv μRadon-Nikodym derivative of the scalar multiple of a measure.
See also rnDeriv_smul_left', which requires sigma-finite ν and μ.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 215 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
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
- NNRealstatement and proof · cited by 4,310
- MeasureTheory.aestatement · cited by 2,352
- Filter.EventuallyEqstatement · cited by 1,912
- ENNReal.ofNNRealproof · cited by 1,279
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- LT.lt.neproof · cited by 872
- Measurable.aemeasurableproof · cited by 304
- MeasureTheory.Measure.withDensityproof · cited by 265
- smul_addproof · cited by 263
Cited by2
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_smul_sameproof · cited by 1
- MeasureTheory.Measure.rnDeriv_smul_left_of_ne_topproof · cited by 1