Functions of $\Phi$-bounded variation and Riemann-Stieltjes integration
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- by Michael Schramm PDF
- Trans. Amer. Math. Soc. 287 (1985), 49-63 Request permission
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.References
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Additional Information
- © Copyright 1985 American Mathematical Society
- Journal: Trans. Amer. Math. Soc. 287 (1985), 49-63
- MSC: Primary 26A45; Secondary 26A42
- DOI: https://doi.org/10.1090/S0002-9947-1985-0766206-3
- MathSciNet review: 766206