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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

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
DOI: https://doi.org/10.1090/S0002-9939-1976-0401993-5
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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DOI: https://doi.org/10.1090/S0002-9939-1976-0401993-5
Article copyright: © Copyright 1976 American Mathematical Society

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