## 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

### Keywords:

partition; selector; $$\sigma$$-filter; $$\sigma$$-field

Zbl 0411.04006
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