Borel classes of uniformizations of sets with large sections

Abstract

We give several refinements of known theorems on Borel uniformizations of sets with "large sections". In particular, we show that a subset B of [0,1]x[0,1], which is of a given additive Borel class and which has "vertical sections" of positive Lebesgue measure, has a uniformization of the corresponding multiplicative Borel class.

Keywords

• Borel sets
• Borel classes
• uniformizations
• sets with large sections
• selections