Theorems · Theorem · measure theory
MeasureTheory.OuterMeasure.le_boundedBy
∀ {α : Type u_1} {m : Set α → ENNReal} {μ : MeasureTheory.OuterMeasure α},
μ ≤ MeasureTheory.OuterMeasure.boundedBy m ↔ ∀ (s : Set α), μ s ≤ m s- Cited by
- 3 results in Mathlib
- Foundations
- Depth 163 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Set.Nonemptyproof · cited by 2,627
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- Set.eq_empty_or_nonemptyproof · cited by 248
- iSup_congr_Propproof · cited by 247
- MeasureTheory.measure_emptyproof · cited by 169
- bot_eq_zero'proof · cited by 92
- iSup_posproof · cited by 61
- iSup_negproof · cited by 49
- MeasureTheory.OuterMeasure.boundedBystatement · cited by 21
Cited by3
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.sInf_eq_boundedBy_sInfGenproof · cited by 2
- MeasureTheory.OuterMeasure.mkMetric_mono_smulproof · cited by 2
- MeasureTheory.OuterMeasure.le_boundedBy'proof · cited by 2