On generalized cluster sets (Q1065954)

In the literature one can find a lot of papers devoted to the boundary behaviour of real functions defined in the upper half-plane. Most of them essentially use the Fubini theorem or Kuratowski-Ulam theorem describing the connections between plane and linear sets of measure zero or of the first category. This paper is devoted to study some generalizations of those limit numbers which are described using the sigma ideals of null or meager sets. In the first part basic facts about product sigma ideals are presented (among others the dependence on the direction of sections) and next some theorems on exceptional sets with respect to boundary behaviour are obtained. Most results are stated without proofs.