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)

Convergence of probability measures on separable Banach spaces


Author: L. Š. Grinblat
Journal: Proc. Amer. Math. Soc. 67 (1977), 321-323
MSC: Primary 60B10
MathSciNet review: 0494377
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: The following result follows immediately from a general theorem on the convergence of probability measures on separable Banach spaces: On the space $ C[0,1]$ there exists a norm $ p(x)$ equivalent to the ordinary norm such that if $ {\xi _1}(t), \ldots ,{\xi _n}(t), \ldots $ and $ \xi (t)$ are continuous random processes $ (0 \leqslant t \leqslant 1)$ and for any finite set of points $ {t_1}, \ldots ,{t_k} \subset [0,1]$ the joint distribution of $ p({\xi _n}),{\xi _n}({t_1}), \ldots ,{\xi _n}({t_k})$ converges to the joint distribution of $ p(\xi ),\xi ({t_1}), \ldots ,\xi ({t_k})$ then $ {\xi _n}(t)$ converges weakly to $ \xi (t)$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B10

Retrieve articles in all journals with MSC: 60B10


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0494377-6
PII: S 0002-9939(1977)0494377-6
Article copyright: © Copyright 1977 American Mathematical Society