Theorems · Theorem · measure theory
isCompact_setOfPred_finiteMeasure_eq_of_compactSpace
∀ (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}In a compact space, the set of finite measures with mass C is compact.
- Defined in
- Mathlib.MeasureTheory.Measure.Prokhorov
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 263 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites16
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Setproof · cited by 53,352
- TopologicalSpacestatement and proof · cited by 24,529
- MeasurableSpacestatement and proof · cited by 13,106
- Set.ofPredstatement and proof · cited by 6,101
- NNRealstatement and proof · cited by 4,310
- BorelSpacestatement and proof · cited by 1,602
- T2Spacestatement and proof · cited by 1,351
- IsCompactstatement and proof · cited by 1,282
- CompactSpacestatement and proof · cited by 593
- continuous_constproof · cited by 278
- MeasureTheory.FiniteMeasurestatement and proof · cited by 150
- isClosed_eqproof · cited by 71
Cited by1
Results whose statement or proof uses this declaration.
- isCompact_setOf_finiteMeasure_eq_of_compactSpaceproof · cited by 0