Of regulated and steplike functions
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- by Gadi Moran PDF
- Trans. Amer. Math. Soc. 231 (1977), 249-257 Request permission
Abstract:
Let C denote the class of regulated real-valued functions on the unit interval vanishing at the origin, whose positive and negative jumps sum to infinity in every nontrivial subinterval of I. Goffman [2] showed that every f in C is (essentially) a sum $g + s$ where g is continuous and s is steplike. In this sense, a function in C is like a function of bounded variation, that has a unique such g and s. The import of this paper is that for f in C the representation $f = g + s$ is not only not unique, but by far the opposite holds: g can be chosen to be any continuous function on I vanishing at 0, at the expense of a rearrangement of s.References
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- Casper Goffman, Gadi Moran, and Daniel Waterman, The structure of regulated functions, Proc. Amer. Math. Soc. 57 (1976), no. 1, 61–65. MR 401993, DOI 10.1090/S0002-9939-1976-0401993-5
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Additional Information
- © Copyright 1977 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 231 (1977), 249-257
- MSC: Primary 26A30
- DOI: https://doi.org/10.1090/S0002-9947-1977-0499028-7
- MathSciNet review: 0499028