Theorems · Theorem · measure theory
MeasureTheory.Content.innerContent_exists_compact
∀ {G : Type w} [inst : TopologicalSpace G] (μ : MeasureTheory.Content G) {U : TopologicalSpace.Opens G},
μ.innerContent U ≠ ⊤ → ∀ {ε : NNReal}, ε ≠ 0 → ∃ K, ↑K ⊆ ↑U ∧ μ.innerContent U ≤ μ K + ↑ε- Defined in
- Mathlib.MeasureTheory.Measure.Content
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 129 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpace
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
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
- Bot.botproof · cited by 4,720
- NNRealstatement and proof · cited by 4,310
- iSupproof · cited by 2,415
- TopologicalSpace.Opensstatement and proof · cited by 2,040
- ENNReal.ofNNRealstatement and proof · cited by 1,279
- le_of_ltproof · cited by 1,175
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.Content.outerMeasure_exists_compactproof · cited by 0