Theorems · Theorem · measure theory
MeasureTheory.Measure.singularPart_smul
∀ {α : Type u_1} {m : MeasurableSpace α} (μ ν : MeasureTheory.Measure α) (r : NNReal),
(r • μ).singularPart ν = r • μ.singularPart ν- Cited by
- 4 results in Mathlib
- Foundations
- Depth 214 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites24
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
- ENNReal.ofNNRealproof · cited by 1,279
- zero_smulproof · cited by 716
- smul_zeroproof · cited by 665
- MeasureTheory.Measure.withDensityproof · cited by 265
- smul_addproof · cited by 263
- MeasureTheory.Measure.rnDerivproof · cited by 234
- MeasureTheory.Measure.HaveLebesgueDecompositionproof · cited by 92
- inv_smul_smul₀proof · cited by 80
Cited by4
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.rnDeriv_smul_leftproof · cited by 2
- MeasureTheory.SignedMeasure.singularPart_smulproof · cited by 1
- MeasureTheory.Measure.rnDeriv_smul_left'proof · cited by 1
- MeasureTheory.SignedMeasure.singularPart_smul_nnrealproof · cited by 1