Theorems · Theorem · measure theory
MeasureTheory.Measure.ae_smul_measure
∀ {α : Type u_1} {R : Type u_6} {m0 : MeasurableSpace α} {μ : MeasureTheory.Measure α} {p : α → Prop}
[inst : SMul R ENNReal] [inst_1 : IsScalarTower R ENNReal ENNReal],
(∀ᵐ (x : α) ∂μ, p x) → ∀ (c : R), ∀ᵐ (x : α) ∂c • μ, p x- Cited by
- 10 results in Mathlib
- Foundations
- Depth 175 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.
Cites11
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
- Set.ofPredproof · cited by 6,101
- IsScalarTowerstatement and proof · cited by 3,896
- Filter.Eventuallystatement and proof · cited by 3,134
- MeasureTheory.aestatement and proof · cited by 2,352
- smul_zeroproof · cited by 665
- smul_one_smulproof · cited by 43
- MeasureTheory.Measure.smul_applyproof · cited by 28
- MeasureTheory.ae_iffproof · cited by 26
Cited by10
Results whose statement or proof uses this declaration.
- ProbabilityTheory.HasLaw.ae_eq_of_smul_diracproof · cited by 2
- MeasureTheory.AEStronglyMeasurable.smul_measureproof · cited by 2
- MeasureTheory.Measure.ae_mem_finset_iffproof · cited by 2
- MeasureTheory.VectorMeasure.integral_diracproof · cited by 2
- MeasureTheory.VectorMeasure.integral_dirac'proof · cited by 2
- MeasureTheory.Measure.ae_smul_measure_leproof · cited by 1
- AEMeasurable.smul_measureproof · cited by 1
- ProbabilityTheory.ae_cond_memproof · cited by 0
- ProbabilityTheory.ae_cond_mem₀proof · cited by 0
- ProbabilityTheory.ae_cond_of_forall_memproof · cited by 0