Convergence of sequences of semi-continuous functions |
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Authors: | JH van der Walt |
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Institution: | Department of Mathematics and Applied Mathematics, University of Pretoria, Pretoria 0002, South Africa |
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Abstract: | In 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. |
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