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2019 Approximations by Differences of Lower Semicontinuous and Finely Continuous Functions
Jaroslav Lukeš, Petr Pošta
Real Anal. Exchange 44(2): 369-382 (2019). DOI: 10.14321/realanalexch.44.2.0369

Abstract

A classical theorem of W.Sierpiński, 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. We 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. Moreover, we examine which topological properties play a crucial role when deriving approximation theorems in more general situations.

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Jaroslav Lukeš. Petr Pošta. "Approximations by Differences of Lower Semicontinuous and Finely Continuous Functions." Real Anal. Exchange 44 (2) 369 - 382, 2019. https://doi.org/10.14321/realanalexch.44.2.0369

Information

Published: 2019
First available in Project Euclid: 1 May 2020

zbMATH: 07211596
Digital Object Identifier: 10.14321/realanalexch.44.2.0369

Subjects:
Primary: 26A15, 26A21, 31C40, 31C45, 31D05, 54E55

Rights: Copyright © 2019 Michigan State University Press

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Vol.44 • No. 2 • 2019
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