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Weak convergence on non-separable metric spaces

Published online by Cambridge University Press:  09 April 2009

David Pollard
David Pollard
Affiliation:
Department of Statistics Yale UniversityNew Haven, CT 06520, USA.
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Abstract

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For certain problems in the weak convergence theory of probability measures on non-separable metric spaces it is convenient to consider measures defined on a σ-field B0 smaller than the Borel σ-field. A suitable theory has been developed by Dudley and Wichura. In this paper it is shown that some of the key results in that theory can be deduced directly from the better known weak convergence theory for Borel measures. This is achieved by a remetrization of the underlying space to make it separable. The σ-field B0 contains the new Borel σ-field and weak convergence in Dudley's sense becomes equivalent to convergence of restrictions of the measures to the latter σ-field.

1980 Mathematics Subject Classification (Amer. Math. Soc.): primary 60 B 10, 60 B 05.

Keywords

weak convergence of non-Borel measuresnon-separable metric spacesσ-field generated by the balls.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 28 , Issue 2 , September 1979 , pp. 197 - 204
Copyright
Copyright © Australian Mathematical Society 1979

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