Geodesic
On the difference property of Borel measurable functions
Hiroshi Fujita 1   ; Tamás Mátrai 2
1 Graduate School of Science and Technology Ehime University Matsuyama 790-8577, Japan
2 Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences Reáltanoda utca 13-15 H-1053 Budapest, Hungary
Fundamenta Mathematicae, Tome 208 (2010) no. 1, pp. 57-73 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/fm208-1-4
Keywords: atomlessly measurable cardinal exists class lebesgue measurable functions class borel functions baire classes orders have difference property gives consistent positive answer laczkovichs problem acta math acad sci hungar complete positive answer laczkovichs problem concerning borel functions baire alpha differences

Hiroshi Fujita  1   ; Tamás Mátrai  2

1 Graduate School of Science and Technology Ehime University Matsuyama 790-8577, Japan
2 Alfréd Rényi Institute of Mathematics Hungarian Academy of Sciences Reáltanoda utca 13-15 H-1053 Budapest, Hungary 
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Hiroshi Fujita; Tamás Mátrai. On the difference property of Borel measurable functions. Fundamenta Mathematicae, Tome 208 (2010) no. 1, pp. 57-73. doi: 10.4064/fm208-1-4

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