Borel classes of uniformizations of sets with large sections

• Autorzy: Petr Holický
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 54H05: Descriptive set theory (topological aspects of Borel, analytic, projective, etc. sets)
• 54E50: Complete metric spaces
• 54C65: Selections

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2010
• Tom: 207
• Numer: 2
• Strony: 145-160

Daty

wydano

2010

Twórcy

autor

Petr Holický

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic

Identyfikatory

DOI

10.4064/fm207-2-3