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Generating Borel sets by balls

Author(s): E. Riss
Translated by: the author
Original publication: Algebra i Analiz, tom 17 (2005), vypusk 4.
Journal: St. Petersburg Math. J. 17 (2006), 683-698.
MSC (2000): Primary 46B20, 46B25, 28A05
Posted: 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.

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Additional Information:

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

DOI: 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): 11/APR/2005
Posted: May 3, 2006
Copyright of article: Copyright 2006, American Mathematical Society

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