Theorems · Theorem · measure theory
MeasureTheory.Measure.rnDeriv_smul_left_of_ne_top
∀ {α : Type u_1} {m : MeasurableSpace α} (ν μ : MeasureTheory.Measure α) [MeasureTheory.IsFiniteMeasure ν]
[ν.HaveLebesgueDecomposition μ] {r : ENNReal}, r ≠ ⊤ → (r • ν).rnDeriv μ =ᵐ[μ] r • ν.rnDeriv μRadon-Nikodym derivative of the scalar multiple of a measure.
See also rnDeriv_smul_left_of_ne_top', which requires sigma-finite ν and μ.
- 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.
Cites12
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
- Top.topstatement and proof · cited by 9,680
- MeasureTheory.aestatement and proof · cited by 2,352
- Filter.EventuallyEqstatement and proof · cited by 1,912
- MeasureTheory.IsFiniteMeasurestatement and proof · cited by 1,078
- MeasureTheory.Measure.rnDerivstatement and proof · cited by 234
- ENNReal.toNNRealproof · cited by 165
- MeasureTheory.Measure.HaveLebesgueDecompositionstatement and proof · cited by 92
- ENNReal.coe_toNNRealproof · cited by 53
- MeasureTheory.Measure.rnDeriv_smul_leftproof · cited by 2
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.llr_smul_leftproof · cited by 2