1976•Proceedings of the American Mathematical SocietyRequires access
The structure of regulated functions
Casper Goffman, Gadi Moran, Daniel Waterman
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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 Φ \Phi -variation for convex Φ \Phi .