Approximation and extension of random functions |
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Authors: | Leon Brown Bertram M Schreiber |
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Affiliation: | (1) Department of Mathematics, Wayne State University, 48202 Detroit, MI, U.S.A |
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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.Research of both authors was partially supported by the NSF under Grant No. DMS 85-02308 |
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