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The Carathéodory extension theorem for vector valued measures


Author: Joseph Kupka
Journal: Proc. Amer. Math. Soc. 72 (1978), 57-61
MSC: Primary 46G10; Secondary 28A45, 60H05
DOI: https://doi.org/10.1090/S0002-9939-1978-0493327-7
MathSciNet review: 0493327
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Abstract: This paper comprises three advertisements for a known theorem which, the author believes, deserves the title of the Carathéodory extension theorem for vector valued premeasures. Principal among these is a short and transparent proof of Porcelli's criterion for the weak convergence of a sequence in the Banach space of bounded finitely additive complex measures defined on an arbitrary field, and equipped with the total variation norm. Also, a characterization of the so-called Carathéodory Extension Property is presented, and there is a brief discussion of the relevance of this material to stochastic integration.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1978-0493327-7
Keywords: Vector valued premeasures, weak convergence of measures, Carathéodory Extension Property, stochastic integration
Article copyright: © Copyright 1978 American Mathematical Society

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