Theorems · Theorem · measure theory
isCompact_setOf_finiteMeasure_le_of_compactSpace
Deprecated since 2026-07-09Use isCompact_setOfPred_finiteMeasure_le_of_compactSpace instead.
∀ (E : Type u_1) [inst : MeasurableSpace E] [inst_1 : TopologicalSpace E] [T2Space E] [inst_3 : BorelSpace E]
[CompactSpace E] (C : NNReal), IsCompact {μ | μ.mass ≤ C}Alias of isCompact_setOfPred_finiteMeasure_le_of_compactSpace.
In a compact space, the set of finite measures with mass at most C is compact.
- Defined in
- Mathlib.MeasureTheory.Measure.Prokhorov
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- TopologicalSpacestatement · cited by 24,529
- MeasurableSpacestatement · cited by 13,106
- Set.ofPredstatement · cited by 6,101
- NNRealstatement · cited by 4,310
- BorelSpacestatement · cited by 1,602
- T2Spacestatement · cited by 1,351
- IsCompactstatement · cited by 1,282
- CompactSpacestatement · cited by 593
- MeasureTheory.FiniteMeasurestatement · cited by 150
- MeasureTheory.FiniteMeasure.massstatement · cited by 46
- isCompact_setOfPred_finiteMeasure_le_of_compactSpaceproof · cited by 3
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