Theorems · Theorem · measure theory
MeasureTheory.OuterMeasure.le_ofFunction
∀ {α : Type u_1} {m : Set α → ENNReal} {m_empty : m ∅ = 0} {μ : MeasureTheory.OuterMeasure α},
μ ≤ MeasureTheory.OuterMeasure.ofFunction m m_empty ↔ ∀ (s : Set α), μ s ≤ m s- Cited by
- 5 results in Mathlib
- Foundations
- Depth 162 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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.iUnionproof · cited by 2,483
- le_transproof · cited by 985
- MeasureTheory.OuterMeasurestatement and proof · cited by 287
- le_iInfproof · cited by 102
- ENNReal.tsum_le_tsumproof · cited by 43
- MeasureTheory.measure_iUnion_leproof · cited by 39
- MeasureTheory.OuterMeasure.monoproof · cited by 36
- MeasureTheory.OuterMeasure.ofFunctionstatement and proof · cited by 21
- MeasureTheory.OuterMeasure.ofFunction_leproof · cited by 10
Cited by5
Results whose statement or proof uses this declaration.
- MeasureTheory.OuterMeasure.le_boundedByproof · cited by 3
- MeasureTheory.OuterMeasure.comap_ofFunctionproof · cited by 2
- MeasureTheory.le_inducedOuterMeasureproof · cited by 1
- MeasureTheory.OuterMeasure.map_ofFunction_leproof · cited by 1
- MeasureTheory.OuterMeasure.isGreatest_ofFunctionproof · cited by 1