On the difference property of Borel measurable functions
Volume 208 / 2010
Fundamenta Mathematicae 208 (2010), 57-73
MSC: 03E15, 28A05, 54H15.
DOI: 10.4064/fm208-1-4
Abstract
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.
