Abstract
Stochastic versions of the extension theorems of Tietze and Dugundji are obtained, as well as an existence theorem for partitions of unity by random continuous functions. A form of the classical approximation theorem of Mergelyan valid for random holomorphic functions on random compact sets is presented. A similar approach yields versions of the approximation theorems of Runge, Arakelyan, and Vitushkin.
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Research of both authors was partially supported by the NSF under Grant No. DMS 85-02308
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Brown, L., Schreiber, B.M. Approximation and extension of random functions. Monatshefte für Mathematik 107, 111–123 (1989). https://doi.org/10.1007/BF01300917
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DOI: https://doi.org/10.1007/BF01300917