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Proceedings of the American Mathematical Society

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The structure of regulated functions

Authors: Casper Goffman, Gadi Moran and Daniel Waterman
Journal: Proc. Amer. Math. Soc. 57 (1976), 61-65
MSC: Primary 26A45
MathSciNet review: 0401993
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Abstract: It is shown that there is a nontrivial class of regulated functions each of which is a representable as the sum of a continuous function and a uniformly convergent series of jump functions whose jumps are those of the given function. The set of regulated functions is the union of the classes of functions of bounded $ \Phi $-variation for convex $ \Phi $.

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  • [3] D. Waterman, On convergence of Fourier series of functions of generalized bounded variation, Studia Math. 44 (1972), 107-117. MR 46 #9623. MR 0310525 (46:9623)

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Article copyright: © Copyright 1976 American Mathematical Society

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