Geodesic
On Uniform Approximations of Abstract Functions
Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 99-108

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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). 
Zakon, Elias. On Uniform Approximations of Abstract Functions. Canadian mathematical bulletin, Tome 10 (1967) no. 1, pp. 99-108. doi: 10.4153/CMB-1967-011-9
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