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Stochastische Analoga des Satzes von Stone-Weierstraß. (Stochastic analogies of the Stone-Weierstraß theorem). (German) Zbl 0744.60012

Stochastic versions of Stone-Weierstrass theorem about uniform approximation of continuous random functions by simpler one’s, are proved. The random functions are defined on arbitrary compact spaces. This generalizes results of O. Onicescu and V. I. Istrăţescu [Rend. Mat., VI. Ser. 8, 65-81 (1975; Zbl 0308.60037)] and V. G. Ryabykh, N. N. Tokmakova and A. Ya. Yablonskij [Mathematical analysis and its applications, Interuniv. Work Collect., Rostov 1985, 131-135 (1985; Zbl 0614.41010)], where stochastic functions on compact sets in \(\mathbb{R}^ n\), \(n\) finite, are examined.

MSC:

60B99 Probability theory on algebraic and topological structures
41A65 Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
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