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Cylindrical probabilities and the differentiation of vector measures

Published online by Cambridge University Press:  22 January 2016

Brian Jefferies
Brian Jefferies*
Affiliation:
Department of Mathematics, University of Wollongong, P. O. Box 1144, Wollongong, N. S. W. 2500, Australia
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There are many results in probability theory on vector spaces which rely implicitly on the approximation of a given cylindrical probability by cylindrical probabilities with moments; for example, this is the basic idea behind the proof of the Radon equivalence of the weak and strong topologies of a metrizable space (Schwartz [13] p. 162). The technique of approximation by cylindrical measures with moments can be systematically developed. In particular, it follows that if each member of a family of cylindrical probabilities with moments is decomposable, then the limits of these cylindrical probabilities are often regular and so they are σ-additive.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 112 , December 1988 , pp. 25 - 51
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

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