Displaying similar documents to “Lebesgue measurability of separately continuous functions and separability.”

On Baire measurable solutions of some functional equations

Karol Baron (2009)

Open Mathematics

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We establish conditions under which Baire measurable solutions f of Γ ( x , y , | f ( x ) - f ( y ) | ) = Φ ( x , y , f ( x + φ 1 ( y ) ) , . . . , f ( x + φ N ( y ) ) ) defined on a metrizable topological group are continuous at zero.

On countable families of sets without the Baire property

Mats Aigner, Vitalij A. Chatyrko, Venuste Nyagahakwa (2013)

Colloquium Mathematicae

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We suggest a method of constructing decompositions of a topological space X having an open subset homeomorphic to the space (ℝⁿ,τ), where n is an integer ≥ 1 and τ is any admissible extension of the Euclidean topology of ℝⁿ (in particular, X can be a finite-dimensional separable metrizable manifold), into a countable family ℱ of sets (dense in X and zero-dimensional in the case of manifolds) such that the union of each non-empty proper subfamily of ℱ does not have the Baire property...