Open Access
2012/2013 Uniform Limits of Preponderantly Continuous Functions
Stanisław Kowalczyk
Real Anal. Exchange 38(1): 241-256 (2012/2013).


There are a few nonequivalent definitions of preponderant continuity \cite{bru1,den1,gra,kow,oma}. In this paper we investigate uniform limits of preponderantly continuous functions. We show that preponderantly continuous functions in the O’Malley sense are closed under uniform limits, while the family of preponderantly continuous functions in the Denjoy sense are not closed under uniform limits and find closure of this family in the topology of uniform convergence. Finally, we prove that the set of preponderantly continuous in Denjoy sense functions is a first category subset of its uniform closure.


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Stanisław Kowalczyk. "Uniform Limits of Preponderantly Continuous Functions." Real Anal. Exchange 38 (1) 241 - 256, 2012/2013.


Published: 2012/2013
First available in Project Euclid: 29 April 2013

zbMATH: 1278.26003
MathSciNet: MR3083208

Primary: 26A15
Secondary: ‎54C30

Keywords: approximate continuity , path continuity , preponderant continuity , uniform limit

Rights: Copyright © 2012 Michigan State University Press

Vol.38 • No. 1 • 2012/2013
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