English
The homeomorphism structure is defined by a pair of continuous maps between ProbabilityMeasure Ω and LevyProkhorov(ProbabilityMeasure Ω).
Русский
Структура гомеоморфизма задаётся парами непрерывных отображений между ProbabilityMeasure Ω и LevyProkhorov(ProbabilityMeasure Ω).
LaTeX
$$$\\mathrm{homeomorph\\_probabilityMeasure\\_levyProkhorov}$ is a definition of a homeomorphism with explicit toFun and invFun.$$
Lean4
/-- The topology of convergence in distribution on a separable Borel space is metrizable. -/
instance instMetrizableSpaceProbabilityMeasure (X : Type*) [TopologicalSpace X] [PseudoMetrizableSpace X]
[SeparableSpace X] [MeasurableSpace X] [BorelSpace X] : MetrizableSpace (ProbabilityMeasure X) :=
by
letI : PseudoMetricSpace X := TopologicalSpace.pseudoMetrizableSpacePseudoMetric X
exact homeomorph_probabilityMeasure_levyProkhorov.isEmbedding.metrizableSpace