On some ideals and related algebras of sets in the plane. (English) Zbl 0726.28003

Balcerzak, Marek

Acta Univ. Carol., Math. Phys. 30, No. 2, 3-7 (1989).

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

Keywords:

algebras of sets in the plane; \(\sigma \) -ideals; meager sets; Lebesgue null sets; Borel sets