Some remarks on functions of -bounded variation

Authors:
S. Perlman and D. Waterman

Journal:
Proc. Amer. Math. Soc. **74** (1979), 113-118

MSC:
Primary 26A45

DOI:
https://doi.org/10.1090/S0002-9939-1979-0521883-X

MathSciNet review:
521883

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Abstract: It is shown that if a function has no external saltus, then its total -variation is independent of its values at points of discontinuity, and a function which is equal to the given function at points of continuity cannot have a lesser total -variation. Necessary and sufficient conditions are determined for one space to contain another and for two spaces to be identical.

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DOI:
https://doi.org/10.1090/S0002-9939-1979-0521883-X

Article copyright:
© Copyright 1979
American Mathematical Society