Theorems · Theorem · measure theory
MeasureTheory.Content.outerMeasure_exists_compact
∀ {G : Type w} [inst : TopologicalSpace G] (μ : MeasureTheory.Content G) [R1Space G] {U : TopologicalSpace.Opens G},
μ.outerMeasure ↑U ≠ ⊤ → ∀ {ε : NNReal}, ε ≠ 0 → ∃ K, ↑K ⊆ ↑U ∧ μ.outerMeasure ↑U ≤ μ.outerMeasure ↑K + ↑ε- Defined in
- Mathlib.MeasureTheory.Measure.Content
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 167 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceR1Space
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Cites21
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 · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- ENNRealstatement and proof · cited by 9,879
- Top.topstatement and proof · cited by 9,680
- SetLike.coestatement and proof · cited by 8,199
- NNRealstatement and proof · cited by 4,310
- le_reflproof · cited by 2,061
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- add_le_addproof · cited by 666
- le_imp_le_of_le_of_leproof · cited by 576
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