Abstract
Let Open image in new window stand for the Fubini-type product of σ-ideals Open image in new window . We consider mixed measure-category σ-ideals Open image in new window and Open image in new window (called the Mendez σ-ideals), and study some features of their structure. We show that Open image in new window and Open image in new window are not invariant with respect to nonzero rotations. Using Fremlin’s results, we describe nice Borel bases of Open image in new window and Open image in new window . The rest of the paper is devoted to uniform versions of the Nikodym theorem and the Lusin theorem for Borel functions of two variables.
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