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Restrictions to continuous functions and Boolean algebras. (English) Zbl 0781.26003

In this paper the author shows that every Borel function \(f: \mathbb{R}\to\mathbb{R}\) is continuous on a set \(A\not\in J\) if \(B(\mathbb{R})/J\) is weakly distributive (\(J\) is a proper ideal of a \(\sigma\)-algebra). Moreover, he investigates some other conditions concerning the problem of restrictions to continuous functions.
Reviewer: R.Pawlak (Łódź)

MSC:

26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
28A10 Real- or complex-valued set functions
06E10 Chain conditions, complete algebras
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