Displaying similar documents to “On Baire approximations of normal integrands”

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.

On Weakly Measurable Functions

Szymon Żeberski (2005)

Bulletin of the Polish Academy of Sciences. Mathematics

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We show that if T is an uncountable Polish space, 𝓧 is a metrizable space and f:T→ 𝓧 is a weakly Baire measurable function, then we can find a meagre set M ⊆ T such that f[T∖M] is a separable space. We also give an example showing that "metrizable" cannot be replaced by "normal".