Lévy–Prokhorov metric

E683051

mathematical concept probability metric

The Lévy–Prokhorov metric is a probability metric on the space of probability measures that metrizes weak convergence and is widely used in probability theory and measure theory.

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Observed surface forms (1)

Surface form	Occurrences
Lévy metric on the real line	1

Statements (37)

Predicate	Object
instanceOf	mathematical concept ⓘ probability metric ⓘ
alternativeName	Lévy–Prokhorov distance NERFINISHED ⓘ
appliesTo	Polish spaces ⓘ metric spaces ⓘ
category	metric on spaces of measures ⓘ
characterizes	tightness of probability measures ⓘ
comparedWith	Fortet–Mourier metric NERFINISHED ⓘ bounded Lipschitz metric ⓘ
definedOn	Borel probability measures ⓘ space of probability measures ⓘ
ensures	equivalence between metric convergence and weak convergence on Polish spaces ⓘ
field	measure theory ⓘ probability theory ⓘ
involves	Borel sigma-algebra NERFINISHED ⓘ probability measure coupling arguments ⓘ
metrizes	convergence in distribution ⓘ weak convergence of probability measures ⓘ
namedAfter	Paul Lévy NERFINISHED ⓘ Yuri Prokhorov NERFINISHED ⓘ
property	complete on suitable spaces of probability measures ⓘ separable on suitable spaces of probability measures ⓘ
relatedTo	Prokhorov’s theorem NERFINISHED ⓘ Skorokhod representation theorem NERFINISHED ⓘ Wasserstein metric NERFINISHED ⓘ total variation distance ⓘ
topologyInduced	weak topology on probability measures ⓘ
usedFor	characterizing weak convergence ⓘ convergence of random variables in distribution ⓘ defining topologies on spaces of probability measures ⓘ stability analysis of stochastic processes ⓘ studying convergence of probability measures ⓘ
usedIn	central limit theorem formulations ⓘ functional limit theorems ⓘ invariance principles ⓘ limit theorems for random measures ⓘ theory of stochastic processes ⓘ

Referenced by (2)

Full triples — surface form annotated when it differs from this entity's canonical label.

Kolmogorov distance → comparedWith → Lévy–Prokhorov metric ⓘ

Kolmogorov distance → strongerThan → Lévy–Prokhorov metric ⓘ

this entity surface form: Lévy metric on the real line