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On extensions of \(\sigma\)-fields of sets. (English) Zbl 0810.28001

The author generalizes a former result by himself and B. Weglorz [J. Aust. Math. Soc., Ser. A 25, 275-290 (1978; Zbl 0411.04006)], concerning the existence of proper \(\sigma\)-fields on the set of real numbers \(\mathbb{R}\), extending a given uniform \(\sigma\)-filter on \(\mathbb{R}\) and a given \(\sigma\)-field \(B\) of subsets of \(\mathbb{R}\), with \(| B|\leq 2^ \omega\), verifying certain properties.

MSC:

28A05 Classes of sets (Borel fields, \(\sigma\)-rings, etc.), measurable sets, Suslin sets, analytic sets

Citations:

Zbl 0411.04006
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