Theorems · Theorem · measure theory
MeasureTheory.Measure.AbsolutelyContinuous.smul_left
∀ {α : Type u_1} {R : Type u_5} {mα : MeasurableSpace α} {μ ν : MeasureTheory.Measure α} [inst : SMul R ENNReal]
[inst_1 : IsScalarTower R ENNReal ENNReal], μ.AbsolutelyContinuous ν → ∀ (c : R), (c • μ).AbsolutelyContinuous ν- Cited by
- 10 results in Mathlib
- Foundations
- Depth 174 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- SMulIsScalarTower
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealstatement and proof · cited by 9,879
- IsScalarTowerstatement and proof · cited by 3,896
- smul_zeroproof · cited by 665
- MeasureTheory.Measure.AbsolutelyContinuousstatement and proof · cited by 325
- smul_one_smulproof · cited by 43
Cited by10
Results whose statement or proof uses this declaration.
- MeasureTheory.Measure.smul_absolutelyContinuousproof · cited by 11
- InformationTheory.toReal_klDiv_smul_right_eq_smul_leftproof · cited by 3
- MeasureTheory.Measure.AbsolutelyContinuous.add_left_iffproof · cited by 3
- MeasureTheory.Measure.MutuallySingular.smulproof · cited by 2
- VitaliFamily.mul_measure_le_of_subset_lt_limRatioMeasproof · cited by 2
- InformationTheory.toReal_klDiv_smul_leftproof · cited by 1
- InformationTheory.toReal_klDiv_smul_sameproof · cited by 1
- MeasureTheory.NullMeasurableSet.smul_measureproof · cited by 1
- VitaliFamily.exists_measurable_supersets_limRatioproof · cited by 1
- InformationTheory.klDiv_smul_right_eq_smul_leftproof · cited by 0