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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
DOI: https://doi.org/10.1090/S0002-9939-1995-1327035-7
MathSciNet review: 1327035
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Abstract | References | Similar Articles | Additional Information

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}$.


References [Enhancements On Off] (What's this?)

  • [1] K. J. Falconer, The geometry of fractal sets, Cambridge Univ. Press, Cambridge and New York, 1985. MR 867284 (88d:28001)
  • [2] S. P. Gudder, Quantum probability spaces, Proc. Amer. Math. Soc. 21 (1969), 296-302. MR 0243793 (39:5114)
  • [3] T. Neubrunn, A note on quantum probability spaces, Proc. Amer. Math. Soc. 25 (1970), 672-675. MR 0259056 (41:3698)
  • [4] V. Olejček, Generation of a q- $ \sigma $-algebra in the plane, Proc. Conf. Topology and Measure V, Wissenshaftliche Beiträge der Ernst-Moritz-Arndt-Universität Greifswald, 1988, pp. 121-125.
  • [5] P. Pták and S. Pulmannová, Orthomodular structures as quantum logics, Kluwer Acad. Publ., Dordrecht, 1991. MR 1176314 (94d:81018b)

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Additional Information

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

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