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-α differences.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-4,
author = {Hiroshi Fujita and Tam\'as M\'atrai},
title = {On the difference property of Borel measurable functions},
journal = {Fundamenta Mathematicae},
volume = {209},
year = {2010},
pages = {57-73},
zbl = {1209.03040},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-4}
}
Hiroshi Fujita; Tamás Mátrai. On the difference property of Borel measurable functions. Fundamenta Mathematicae, Tome 209 (2010) pp. 57-73. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-fm208-1-4/