# Wydawnictwa / Czasopisma IMPAN / Fundamenta Mathematicae / Wszystkie zeszyty

## On the difference property of Borel measurable functions

### Tom 208 / 2010

Fundamenta Mathematicae 208 (2010), 57-73 MSC: 03E15, 28A05, 54H15. DOI: 10.4064/fm208-1-4

#### Streszczenie

If an atomlessly measurable cardinal exists, then the class of Lebesgue measurable functions, the class of Borel functions, and the Baire classes of all orders have the difference property. This gives a consistent positive answer to Laczkovich's Problem 2 [Acta Math. Acad. Sci. Hungar. 35 (1980)]. We also give a complete positive answer to Laczkovich's Problem 3 concerning Borel functions with Baire-$\alpha$ differences.

#### Autorzy

• Hiroshi FujitaGraduate School of Science and Technology
Ehime University
Matsuyama 790-8577, Japan
e-mail
• Tamás MátraiAlfréd Rényi Institute of Mathematics