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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 $ \sigma$-class generated by balls contains all Borel sets


Author: Vladimír Olejček
Journal: Proc. Amer. Math. Soc. 123 (1995), 3665-3675
MSC: Primary 28A05; Secondary 04A03
MathSciNet review: 1327035
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Abstract: The $ \sigma $-class, i.e. the system of sets closed under complementation, countable disjoint unions and containing the empty set, generated by the system of open balls coincides with the $ \sigma $-field of Borel sets in $ {\mathbb{R}^3}$.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1995-1327035-7
PII: S 0002-9939(1995)1327035-7
Keywords: $ \sigma $-class, concrete quantum logic, Borel sets, fractal, ball, net
Article copyright: © Copyright 1995 American Mathematical Society