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