A note on weak convergence

A note on weak convergence

We show that in a Polish space if {P n } is a sequence of probability measures then the existence of ${\lim _n}\int {fd{P_n}} $ for every bounded continuous function guarantees the existence of a probability P such that P n converges weakly to P.

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Veröffentlicht in:Sankhya. Series. A 2012-08, Vol.74 (2), p.269-276
Hauptverfasser: Ramamoorthi, R.V., Rao, B.V., Sethuraman, J.
Format: Artikel
Sprache:eng
Schlagworte:
Continuous functions
Convergence
Integers
Mathematical functions
Mathematical theorems
Mathematics and Statistics
Perceptron convergence procedure
Probability
Real lines
Separable spaces
Statistical Theory and Methods
Statistics
Statistics and Computing/Statistics Programs
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Zusammenfassung:We show that in a Polish space if {P n } is a sequence of probability measures then the existence of ${\lim _n}\int {fd{P_n}} $ for every bounded continuous function guarantees the existence of a probability P such that P n converges weakly to P.
ISSN:0976-836X
0976-8378
DOI:10.1007/s13171-012-0016-6