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Transactions of the American Mathematical Society
Transactions of the American Mathematical Society
ISSN 1088-6850(online) ISSN 0002-9947(print)

 

Functions of $ \Phi$-bounded variation and Riemann-Stieltjes integration


Author: Michael Schramm
Journal: Trans. Amer. Math. Soc. 287 (1985), 49-63
MSC: Primary 26A45; Secondary 26A42
MathSciNet review: 766206
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Abstract: A notion of generalized bounded variation is introduced which simultaneously generalizes many of those previously examined. It is shown that the class of functions arising from this definition is a Banach space with a suitable norm. Appropriate variation functions are defined and examined, and an analogue of Helly's theorem is estabished. The significance of this class to convergence of Fourier series is briefly discussed. A result concerning Riemann-Stieltjes integrals of functions of this class is proved.


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DOI: http://dx.doi.org/10.1090/S0002-9947-1985-0766206-3
PII: S 0002-9947(1985)0766206-3
Article copyright: © Copyright 1985 American Mathematical Society