Displaying similar documents to “A measurable selection theorem”

On the difference property of Borel measurable functions

Hiroshi Fujita, Tamás Mátrai (2010)

Fundamenta Mathematicae

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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-α differences.

Functions Equivalent to Borel Measurable Ones

Andrzej Komisarski, Henryk Michalewski, Paweł Milewski (2010)

Bulletin of the Polish Academy of Sciences. Mathematics

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Let X and Y be two Polish spaces. Functions f,g: X → Y are called equivalent if there exists a bijection φ from X onto itself such that g∘φ = f. Using a theorem of J. Saint Raymond we characterize functions equivalent to Borel measurable ones. This characterization answers a question asked by M. Morayne and C. Ryll-Nardzewski.