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Keywords:
regulated functions; linear prolongation along an increasing function; analogue of Helley's principle of choice theorem; Banach space
regulated functions; linear prolongation along an increasing function; analogue of Helley's principle of choice theorem; Banach space
Summary:
The first section consists of auxiliary results about nondecreasing real functions. In the second section a new characterization of relatively compact sets of regulated functions in the sup-norm topology is brought, and the third section includes, among others, an analogue of Helly's Choice Theorem in the space of regulated functions.
References:
[1] G. Aumann: Reelle Funktionen. Springer-Verlag, Berlin, Heidelberg, New York 1969. MR 0061652 | Zbl 0181.05801
[2] I. I. Gichman A. V. Skorochod: Theory of Stochastic Processes. (Russian). Nauka, Moskva 1971.
[3] Ch. S. Hönig: Volterra-Stieltjes-Integral equations. North Holland, American Elsevier 1975. MR 0499969
[4] Ch. S. Hönig: Equations integrales generalisées et aplications. Publications mathématiques d'Orsay, Orsay 1982. MR 0697399
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