Wolnicka
Abstract
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In the paper it is shown that the strongly quasi-uniform limit of a sequence of 1-improvable discontinuous functions on a complete space \(X\) is a 1-improvable discontinuous function or a continuous function. Automatically the same result will be valid for uniform convergence.
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In the paper it is shown that the strongly quasi-uniform limit of a sequence of 1-improvable discontinuous functions on a complete space \(X\) is a 1-improvable discontinuous function or a continuous function. Automatically the same result will be valid for uniform convergence.
Key concepts: Uniform limit theorem, Mathematics, Uniform convergence, Sequence (biology), Convergence (economics), Limit (mathematics), Modes of convergence (annotated index), Limit of a sequence