Theorems · Theorem · measure theory
MeasureTheory.Measure.smul_apply
∀ {α : Type u_1} {R : Type u_6} [inst : SMul R ENNReal] [inst_1 : IsScalarTower R ENNReal ENNReal]
{_m : MeasurableSpace α} (c : R) (μ : MeasureTheory.Measure α) (s : Set α), (c • μ) s = c • μ s- Cited by
- 28 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.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Setstatement and proof · 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
Cited by28
Results whose statement or proof uses this declaration.
- ProbabilityTheory.cond_applyproof · cited by 20
- MeasureTheory.Measure.ae_smul_measureproof · cited by 10
- MeasureTheory.setToFun_congr_measure_of_integrableproof · cited by 5
- MeasureTheory.Measure.AbsolutelyContinuous.smulproof · cited by 4
- MeasureTheory.Measure.prod_smul_leftproof · cited by 3
- MeasureTheory.Measure.toSphere_apply'proof · cited by 3
- MeasureTheory.Measure.OuterRegular.smulproof · cited by 2
- Ergodic.of_mem_extremePoints_measure_univ_eqproof · cited by 2
- MeasureTheory.pdf.IsUniform.aemeasurableproof · cited by 2
- MeasureTheory.Measure.InnerRegularWRT.smulproof · cited by 2
- MeasureTheory.measure_eq_sub_vaddproof · cited by 2
- AddMonoidHom.measurePreservingproof · cited by 2