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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



On the extension of cylinder measures to $ \tau $-smooth measures in linear spaces

Author: Dirk Heidemann
Journal: Proc. Amer. Math. Soc. 61 (1976), 59-65
MSC: Primary 28A40; Secondary 60B05
MathSciNet review: 0422562
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Abstract: We give a necessary and sufficient condition for a cylindrical probability measure in the weak$ ^{\ast}$-dual of an arbitrary l.c.s. to extend to a $ \tau $-smooth Borel-measure; this is to a certain extent a ``$ \tau $-smooth analogue'' of the well-known Prohorov extension theorem (cf. [8, Lemma 3]). Finally, we give two examples marking off our result from related ones treated in the literature.

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Keywords: Linear stochastic processes, extension of cylinder measures in linear spaces, $ \tau $-smooth measures in topological vector spaces, Prohorov's extension theorem
Article copyright: © Copyright 1976 American Mathematical Society