Theorems · Theorem · measure theory
isCompact_closure_of_isTightMeasureSet
- 1000+ list: Prokhorov's theorem
∀ {E : Type u_1} [inst : MeasurableSpace E] [inst_1 : TopologicalSpace E] [T2Space E] [inst_3 : BorelSpace E]
{S : Set (MeasureTheory.ProbabilityMeasure E)},
MeasureTheory.IsTightMeasureSet {x | ∃ μ ∈ S, ↑μ = x} → IsCompact (closure S)Prokhorov theorem: the closure of a tight set of probability measures is compact. We only require the space to be T2.
- Defined in
- Mathlib.MeasureTheory.Measure.Prokhorov
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 267 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites38
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
- Set.ofPredstatement and proof · cited by 6,101
- nhdsproof · cited by 5,554
- NNRealproof · cited by 4,310
- Filter.Tendstoproof · cited by 3,814
- LE.le.transproof · cited by 3,151
- Compl.complproof · cited by 2,925
Cited by1
Results whose statement or proof uses this declaration.
- MeasureTheory.ProbabilityMeasure.tendsto_of_tight_of_separatesPointsproof · cited by 1