Geodesics and generalized geodesics: Difference between revisions
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== Statement == | == Statement == | ||
: '''Theorem.'''<ref name=Santambrogio /> Let <math> \mu_{n} </math> be a sequence of tight probability measures on Polish space <math> X </math>. Then, there exists <math> \mu \in P(X) </math> and convergent subsequence <math> \mu_{n_{k}}</math> such that <math> \mu_{n_{k}} \rightarrow \mu </math> in the dual of <math> C_{b}(X) </math>. Conversely, every sequence <math> \mu_{n} \rightarrow \mu </math> is tight. | : '''Theorem.'''(Benamow-Brenier)<ref name=Santambrogio /> Let <math> \mu_{n} </math> be a sequence of tight probability measures on Polish space <math> X </math>. Then, there exists <math> \mu \in P(X) </math> and convergent subsequence <math> \mu_{n_{k}}</math> such that <math> \mu_{n_{k}} \rightarrow \mu </math> in the dual of <math> C_{b}(X) </math>. Conversely, every sequence <math> \mu_{n} \rightarrow \mu </math> is tight. | ||
= References = | = References = | ||
Revision as of 11:15, 8 June 2020
Statement
- Theorem.(Benamow-Brenier)[1] Let be a sequence of tight probability measures on Polish space . Then, there exists and convergent subsequence such that in the dual of . Conversely, every sequence is tight.
