Measure-category properties of Borel plane sets and Borel functions of two variables
by
Marek Balcerzak
Institute of Mathematics, Technical University of Łódź
Coauthors: Szymon Głąb

Let I⊗J stand for the Fubini-type product of s-ideals I, J ⊂ P(R). We consider mixed measure-category s-ideals M⊗N and N⊗M (called the Mendez s-ideals). We study some features of their structure. We show that M⊗N and N⊗M are not invariant with respect to nonzero rotations. Using Fremlin's results, we describe nice Borel bases of M⊗N, N⊗M, {∅}⊗N and {∅}⊗M. The remaining results are devoted to parametric versions of the Nikodym theorem and the Lusin theorem for Borel functions of two variables.

Date received: June 25, 2008