Borel Classes of Uniformizations of Sets with Large Sections
نویسنده
چکیده
We give several refinements of known theorems on Borel uniformizations of sets with ”large sections”. In particular, we show that a set B ⊂ [0, 1] × [0, 1] which belongs to Σ0α, α ≥ 2, and which has all ”vertical” sections of positive Lebesgue measure, has a Π0α uniformization which is the graph of a Σ0α-measurable mapping. We get a similar result for sets with nonmeager sections. As a corollary we derive an improvement of Srivastava’s theorem on uniformizations for Borel sets with Gδ sections.
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