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Approximations by differences of lower semicontinuous and finely continuous functions. (English) Zbl 07211596
A classical theorem of W.Sierpi’nski, S. Mazurkiewicz and S.Kempisty says that the class of all differences of lower semicontinuous functions is uniformly dense in the space of all Baire-one functions. Here the authors show a generalization of this result to the case when finely continuous functions of either density topologies or both linear and nonlinear potential theory are involved.
26A15 Continuity and related questions (modulus of continuity, semicontinuity, discontinuities, etc.) for real functions in one variable
26A21 Classification of real functions; Baire classification of sets and functions
31C40 Fine potential theory; fine properties of sets and functions
Full Text: DOI Euclid
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