Functions of Φ-bounded variation and Riemann-Stieltjes integration

Schramm, Michael

doi:10.1090/S0002-9947-1985-0766206-3

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

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Sur une généralisation de la notion de variation de puissance

ième bornée au sens de M. Wiener, et sur la convergence des séries de Fourier

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