Some remarks on functions of Λ-bounded variation

Perlman, S.; Waterman, D.

doi:10.1090/S0002-9939-1979-0521883-X

Some remarks on functions of $\Lambda$-bounded variation
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by S. Perlman and D. Waterman

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

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

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Abstract:

It is shown that if a $\Lambda {\text {BV}}$ function has no external saltus, then its total $\Lambda$-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 $\Lambda$-variation. Necessary and sufficient conditions are determined for one $\Lambda {\text {BV}}$ space to contain another and for two spaces to be identical.

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