Theorems · Theorem · measure theory
MeasureTheory.Measure.InnerRegularWRT.isCompact_isClosed
∀ {X : Type u_3} [inst : TopologicalSpace X] [SigmaCompactSpace X] [inst_2 : MeasurableSpace X]
(μ : MeasureTheory.Measure X), μ.InnerRegularWRT IsCompact IsClosedIn a σ-compact space, any closed set can be approximated by a compact subset.
- Defined in
- Mathlib.MeasureTheory.Measure.Regular
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 200 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites24
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- MeasureTheory.Measurestatement and proof · cited by 10,939
- ENNRealproof · cited by 9,879
- Set.iUnionproof · cited by 2,483
- iSupproof · cited by 2,415
- IsClosedstatement and proof · cited by 1,639
- IsCompactstatement and proof · cited by 1,282
- Set.inter_subset_leftproof · cited by 360
- Set.inter_univproof · cited by 198
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