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)

 

Another interesting property concerning the probability measures on the rationals


Author: K. W. Lane
Journal: Proc. Amer. Math. Soc. 87 (1983), 717-722
MSC: Primary 60B05; Secondary 28C15, 54H05
MathSciNet review: 687649
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Let $ X$ be a perfect, complete, separable metric space and $ P(X)$ denote the space of Borel probability measures on $ X$ equipped with the topology of weak convergence. If $ Y$ is a countable dense subset of $ X$ then $ P(Y)$ is not a $ {G_{\delta \sigma }}$ subset of $ P(X)$. Furthermore if $ X$ is separable, complete and metric, and $ Y \subseteq X$, and $ P(Y)$ is a $ {G_{\delta \sigma }}$ subset of $ P(X)$, then $ P(Y)$ is in fact a $ {G_\delta }$ subset of $ P(X)$.


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


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 60B05, 28C15, 54H05

Retrieve articles in all journals with MSC: 60B05, 28C15, 54H05


Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1983-0687649-6
PII: S 0002-9939(1983)0687649-6
Article copyright: © Copyright 1983 American Mathematical Society