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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Some remarks on functions of $ \Lambda $-bounded variation


Authors: S. Perlman and D. Waterman
Journal: Proc. Amer. Math. Soc. 74 (1979), 113-118
MSC: Primary 26A45
MathSciNet review: 521883
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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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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0521883-X
PII: S 0002-9939(1979)0521883-X
Article copyright: © Copyright 1979 American Mathematical Society