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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.
MSC:
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
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