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On Uniform Approximations of Abstract Functions

Published online by Cambridge University Press:  20 November 2018

Elias Zakon
Elias Zakon*
Affiliation:
University of Windsor, CanadaSummer Research Institute of the Canadian Mathematical Congress
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As is well known, every real function is the pointwise (uniform) limit of a sequence of functions with a finite (countable) range of values. Monna [5] and Kvačko [4] suggested some extensions of this theorem to functions with values in a separable metric space. In the present note we give some further generalizations, with an emphasis on uniform approximations which have many applications in the generalized theory of measure and integration. In particular, we consider measurable abstract functions (mappings).

Type
Research Article
Information
Canadian Mathematical Bulletin , Volume 10 , Issue 1 , April 1967 , pp. 99 - 108
Copyright
Copyright © Canadian Mathematical Society 1967

References

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