Van der Walt, Jan Harm2017-01-102017-01-102012-04Van der Walt, JH 2012, 'Convergence of sequences of semi-continuous functions', Journal of Mathematical Analysis and Applications, vol. 388, no. 2, pp. 739-752.0022-247X (print)1096-0813 (online)10.1016/j.jmaa.2011.09.063http://hdl.handle.net/2263/58463In 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© 2011 Elsevier Inc. All rights reserved. This is an open access article under an Elsevier user license.Semi-continuous functionsOrder convergencePointwise convergenceContinuous convergenceArticle