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St. Petersburg Mathematical Journal
St. Petersburg Mathematical Journal
ISSN 1547-7371(online) ISSN 1061-0022(print)

Generating Borel sets by balls


Author: E. Riss
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), nomer 4.
Journal: St. Petersburg Math. J. 17 (2006), 683-698
MSC (2000): Primary 46B20, 46B25, 28A05
Published electronically: May 3, 2006
MathSciNet review: 2173940
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Abstract | References | Similar Articles | Additional Information

Abstract: It is proved that an arbitrary infinite-dimensional Banach space with basis admits an equivalent norm such that any Borel set can be obtained from balls by taking complements and countable disjoint unions. For reflexive spaces, the new norm can be chosen arbitrarily close to the initial norm.


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Additional Information

E. Riss
Affiliation: Russian State Pedagogical University, Moĭka 48, St. Petersburg 191186, Russia

DOI: http://dx.doi.org/10.1090/S1061-0022-06-00925-3
PII: S 1061-0022(06)00925-3
Keywords: Dynkin system, monotone system, small balls, large balls, Borel sets
Received by editor(s): April 11, 2005
Published electronically: May 3, 2006
Article copyright: © Copyright 2006 American Mathematical Society