Theorems · Definition · measure theory
MeasureTheory.OuterMeasure.ofFunction
{α : Type u_1} → (m : Set α → ENNReal) → m ∅ = 0 → MeasureTheory.OuterMeasure αGiven any function m assigning measures to sets satisfying m ∅ = 0, there is
a unique maximal outer measure μ satisfying μ s ≤ m s for all s : Set α.
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 160 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setstatement and proof · cited by 53,352
- ENNRealstatement and proof · cited by 9,879
- Set.iUnionproof · cited by 2,483
- SummationFilter.unconditionalproof · cited by 2,068
- iInfproof · cited by 1,690
- tsumproof · cited by 1,148
- MeasureTheory.OuterMeasurestatement · cited by 287
Cited by24
Results whose statement or proof uses this declaration.
- MeasureTheory.inducedOuterMeasureproof · cited by 22
- MeasureTheory.OuterMeasure.boundedByproof · cited by 21
- MeasureTheory.OuterMeasure.ofFunction_lestatement · cited by 10
- StieltjesFunction.outerproof · cited by 6
- MeasureTheory.OuterMeasure.le_ofFunctionstatement and proof · cited by 5
- MeasureTheory.OuterMeasure.ofFunction_eqstatement · cited by 3
- MeasureTheory.OuterMeasure.ofFunction_applystatement · cited by 2
- MeasureTheory.OuterMeasure.ofFunction_caratheodorystatement and proof · cited by 2
- MeasureTheory.OuterMeasure.ofFunction_eq_iInf_memstatement · cited by 2
- MeasureTheory.OuterMeasure.ofFunction_union_of_top_of_nonempty_interstatement and proof · cited by 2
- MeasureTheory.OuterMeasure.comap_ofFunctionstatement and proof · cited by 2
- MeasureTheory.OuterMeasure.ofFunction.congr_simpstatement and proof · cited by 2