The Carathéodory extension theorem for vector valued measures
Author:
Joseph Kupka
Journal:
Proc. Amer. Math. Soc. 72 (1978), 5761
MSC:
Primary 46G10; Secondary 28A45, 60H05
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 socalled Carathéodory Extension Property is presented, and there is a brief discussion of the relevance of this material to stochastic integration.
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 S. Gaina, Extension of vector measures, Rev. Roumaine Math. Pures et Appl. 8 (1963), 151154. MR 0163998 (29:1297)
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 I. Kluvánek, The extension and closure of vector measure, Vector and Operator Valued Measures and Applications (Proc. Sympos., Alta, Utah, 1972), Academic Press, New York, 1973, pp. 175190. MR 0335741 (49:521)
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 M. Metivier, Stochastic integral and vector valued measures, Vector and Operator Valued Measures and Applications (Proc. Sympos., Alta, Utah, 1972), Academic Press, New York, 1973, pp. 283296. MR 0331509 (48:9842)
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939197804933277
PII:
S 00029939(1978)04933277
Keywords:
Vector valued premeasures,
weak convergence of measures,
Carathéodory Extension Property,
stochastic integration
Article copyright:
© Copyright 1978
American Mathematical Society
