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On some ideals and related algebras of sets in the plane. (English) Zbl 0726.28003
By K and L we denote, respectively, the $$\sigma$$-ideals of meager sets and Lebesgue null sets in $$I=[0,1].$$ Let us denote by (KL) [resp. (LK)] the $$\sigma$$-algebra generated by Borel sets in $$I^ 2$$ and by sets from $$K\otimes L$$ $$[resp.\quad L\otimes K].$$ The author shows that each set from (KL) [resp. (LK)] is contained in a special simple set from (KL) [resp. (LK)] such that the difference of the sets is small.
##### MSC:
 28A05 Classes of sets (Borel fields, $$\sigma$$-rings, etc.), measurable sets, Suslin sets, analytic sets
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