Theorems · Theorem · measure theory
MeasureTheory.IsTightMeasureSet.of_compactSpace
∀ {𝓧 : Type u_1} {m𝓧 : MeasurableSpace 𝓧} {S : Set (MeasureTheory.Measure 𝓧)} [inst : TopologicalSpace 𝓧]
[CompactSpace 𝓧], MeasureTheory.IsTightMeasureSet SIn a compact space, every set of measures is tight.
- Defined in
- Mathlib.MeasureTheory.Measure.Tight
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 171 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- TopologicalSpaceCompactSpace
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Cites20
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- Setstatement and proof · 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
- nhdsproof · cited by 5,554
- Filter.Tendstoproof · cited by 3,814
- iSupproof · cited by 2,415
- CompactSpacestatement and proof · cited by 593
- iSup_congr_Propproof · cited by 247
- MeasureTheory.measure_emptyproof · cited by 169
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