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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

A type of Strassen's theorem for positive vector measures with values in dual spaces


Author: Jun Kawabe
Journal: Proc. Amer. Math. Soc. 128 (2000), 3291-3300
MSC (2000): Primary 28B05, 28A33; Secondary 46A40
Published electronically: April 28, 2000
MathSciNet review: 1670387
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Abstract:

In this paper, we extend a type of Strassen's theorem for the existence of probability measures with given marginals to positive vector measures with values in the dual of a barreled locally convex space which has certain order conditions. In this process of the extension we also give some useful properties for vector measures with values in dual spaces.


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Additional Information

Jun Kawabe
Affiliation: Department of Mathematics, Faculty of Engineering, Shinshu University, 4-17-1 Wakasato, Nagano 380-8553, Japan
Email: jkawabe@gipwc.shinshu-u.ac.jp

DOI: http://dx.doi.org/10.1090/S0002-9939-00-05384-3
PII: S 0002-9939(00)05384-3
Keywords: Strassen's theorem, positive vector measure, weak convergence of vector measures, barreled locally convex space, Riesz space
Received by editor(s): July 9, 1998
Received by editor(s) in revised form: December 20, 1998
Published electronically: April 28, 2000
Additional Notes: This research was supported by Grant-in-Aid for General Scientific Research No.\ 11640160, the Ministry of Education, Science, Sports and Culture, Japan.
Communicated by: Dale Alspach
Article copyright: © Copyright 2000 American Mathematical Society