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

Author(s): Miroslav Zelený
Journal: Proc. Amer. Math. Soc. 128 (2000), 433-437.
MSC (1991): Primary 28A05, 04A15
Posted: September 23, 1999
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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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V. Olej\v{c}ek, The $\sigma $-class generated by balls contains all Borel sets, Proc. Amer. Math. Soc. 123 (12) (1995), 3665-3675. MR 96c:28001

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D. Preiss, T. Keleti, The balls do not generate all Borel sets using complements and countable disjoint unions (to appear).

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D. Preiss, J. Ti\v{s}er, Measures in Banach spaces are determined by their values on balls, Mathematika 38 (1991), 391-397. MR 93a:46080

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W. Ziemer, Weakly differentiable functions, Springer-Verlag, 1989. MR 91e:46046

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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: 10.1090/S0002-9939-99-05507-0
PII: S 0002-9939(99)05507-0
Received by editor(s): February 11, 1998
Posted: September 23, 1999
Additional Notes: This research was supported by Research Grant GAUK 190/1996 and GACR 201/97/1161.
Communicated by: Frederick W. Gehring
Copyright of article: Copyright 1999, American Mathematical Society

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