Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
MathSciNet review: 0493327
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

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.


References [Enhancements On Off] (What's this?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 46G10, 28A45, 60H05

Retrieve articles in all journals with MSC: 46G10, 28A45, 60H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1978-0493327-7
PII: S 0002-9939(1978)0493327-7
Keywords: Vector valued premeasures, weak convergence of measures, Carathéodory Extension Property, stochastic integration
Article copyright: © Copyright 1978 American Mathematical Society