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

 

The Dynkin system generated by balls in $\mathbb{R}^{d}$ contains all Borel sets


Author: Miroslav Zelený
Journal: Proc. Amer. Math. Soc. 128 (2000), 433-437
MSC (1991): Primary 28A05, 04A15
Published electronically: September 23, 1999
MathSciNet review: 1695330
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Abstract: We show that for every $d \in \mathbb{N}$ each Borel subset of the space $\mathbb{R}^{d}$ with the Euclidean metric can be generated from closed balls by complements and countable disjoint unions.


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Additional Information

Miroslav Zelený
Affiliation: Faculty of Mathematics and Physics, Charles University, Sokolovská 83, Prague 186 00, Czech Republic
Email: zeleny@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-99-05507-0
PII: S 0002-9939(99)05507-0
Received by editor(s): February 11, 1998
Published electronically: September 23, 1999
Additional Notes: This research was supported by Research Grant GAUK 190/1996 and GAČR 201/97/1161.
Communicated by: Frederick W. Gehring
Article copyright: © Copyright 1999 American Mathematical Society