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.

Bibliographische Detailangaben

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
Online-Zugang:	Volltext
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