# Borel classes of uniformizations of sets with large sections

Fundamenta Mathematicae (2010)

- Volume: 207, Issue: 2, page 145-160
- ISSN: 0016-2736

## Access Full Article

top## Abstract

top## How to cite

topPetr 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 -

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.