Convergence of sequences of semi-continuous functions

dc.contributor.authorVan der Walt, Jan Harm
dc.contributor.emailjanharm.vanderwalt@up.ac.zaen_ZA
dc.date.accessioned2017-01-10T09:59:52Z
dc.date.available2017-01-10T09:59:52Z
dc.date.issued2012-04
dc.description.abstractIn this paper we investigate how three well-known modes of convergence for (real-valued) functions are related to one another. In particular, we consider order convergence, pointwise convergence and continuous convergence of sequences of nearly finite normal lower semi-continuous functions. There is a natural comparison to be made between the results we obtain for convergence of sequences of semi-continuous functions, and classic results on the convergence of sequences of measurable functions.en_ZA
dc.description.departmentMathematics and Applied Mathematicsen_ZA
dc.description.librarianhb2016en_ZA
dc.description.urihttp://www.elsevier.com/locate/jmaaen_ZA
dc.identifier.citationVan der Walt, JH 2012, 'Convergence of sequences of semi-continuous functions', Journal of Mathematical Analysis and Applications, vol. 388, no. 2, pp. 739-752.en_ZA
dc.identifier.issn0022-247X (print)
dc.identifier.issn1096-0813 (online)
dc.identifier.other10.1016/j.jmaa.2011.09.063
dc.identifier.urihttp://hdl.handle.net/2263/58463
dc.language.isoenen_ZA
dc.publisherElsevieren_ZA
dc.rights© 2011 Elsevier Inc. All rights reserved. This is an open access article under an Elsevier user license.en_ZA
dc.subjectSemi-continuous functionsen_ZA
dc.subjectOrder convergenceen_ZA
dc.subjectPointwise convergenceen_ZA
dc.subjectContinuous convergenceen_ZA
dc.titleConvergence of sequences of semi-continuous functionsen_ZA
dc.typeArticleen_ZA

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