Generating Borel sets by balls
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E. Riss
Translated by: the author - St. Petersburg Math. J. 17 (2006), 683-698
- DOI: https://doi.org/10.1090/S1061-0022-06-00925-3
- Published electronically: May 3, 2006
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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.References
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Bibliographic Information
- E. Riss
- Affiliation: Russian State Pedagogical University, Moĭka 48, St. Petersburg 191186, Russia
- Received by editor(s): April 11, 2005
- Published electronically: May 3, 2006
- © Copyright 2006 American Mathematical Society
- Journal: St. Petersburg Math. J. 17 (2006), 683-698
- MSC (2000): Primary 46B20, 46B25, 28A05
- DOI: https://doi.org/10.1090/S1061-0022-06-00925-3
- MathSciNet review: 2173940