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 , α ≥ 2, and which has all “vertical” sections of positive Lebesgue measure, has a uniformization which is the graph of a -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 sections.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-2-3,
author = {Petr Holick\'y},
title = {Borel classes of uniformizations of sets with large sections},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {145-160},
zbl = {1193.54020},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-2-3}
}
Petr Holický. Borel classes of uniformizations of sets with large sections. Fundamenta Mathematicae, Tome 209 (2010) pp. 145-160. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm207-2-3/