Borel classes of uniformizations of sets with large sections

Petr Holický. "Borel classes of uniformizations of sets with large sections." Fundamenta Mathematicae 207.2 (2010): 145-160. <http://eudml.org/doc/283087>.

@article{PetrHolický2010,
abstract = {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 $Σ⁰_\{α\}$, α ≥ 2, and which has all “vertical” sections of positive Lebesgue measure, has a $Π⁰_\{α\}$ uniformization which is the graph of a $Σ⁰_\{α\}$-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 $G_\{δ\}$ sections.},
author = {Petr Holický},
journal = {Fundamenta Mathematicae},
keywords = {Borel classes; sets with large sections; uniformizations; selections},
language = {eng},
number = {2},
pages = {145-160},
title = {Borel classes of uniformizations of sets with large sections},
url = {http://eudml.org/doc/283087},
volume = {207},
year = {2010},
}

TY - JOUR
AU - Petr Holický
TI - Borel classes of uniformizations of sets with large sections
JO - Fundamenta Mathematicae
PY - 2010
VL - 207
IS - 2
SP - 145
EP - 160
AB - 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 $Σ⁰_{α}$, α ≥ 2, and which has all “vertical” sections of positive Lebesgue measure, has a $Π⁰_{α}$ uniformization which is the graph of a $Σ⁰_{α}$-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 $G_{δ}$ sections.
LA - eng
KW - Borel classes; sets with large sections; uniformizations; selections
UR - http://eudml.org/doc/283087
ER -