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

   

 

Borel complexity of the space of probability measures


Author: Abhijit Dasgupta
Journal: Proc. Amer. Math. Soc. 129 (2001), 2441-2443
MSC (2000): Primary 03E15, 60B05; Secondary 28A05
Published electronically: January 23, 2001
MathSciNet review: 1823929
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Abstract:

Using a technique developed by Louveau and Saint Raymond, we find the complexity of the space of probability measures in the Borel hierarchy: if $X$ is any non-Polish Borel subspace of a Polish space, then $P(X)$, the space of probability Borel measures on $X$ with the weak topology, is always true ${\boldsymbol{\Pi}^{\boldsymbol{0}}_{\boldsymbol{\xi}}}$, where $\xi$ is the least ordinal such that $X$ is ${\boldsymbol{\Pi}^{\boldsymbol{0}}_{\boldsymbol{\xi}}}$.


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Additional Information

Abhijit Dasgupta
Email: takdoom@yahoo.com

DOI: http://dx.doi.org/10.1090/S0002-9939-01-05801-4
PII: S 0002-9939(01)05801-4
Keywords: Descriptive set theory, probability measures, Borel complexity
Received by editor(s): October 24, 1994
Received by editor(s) in revised form: November 24, 1999
Published electronically: January 23, 2001
Additional Notes: Supported in part by NSF Grant # DMS-9214048.
Communicated by: Andreas R. Blass
Article copyright: © Copyright 2001 Abhijit Dasgupta, GNU GPL style copyleft