Abstract
We obtain sufficient conditions of existence of the Stieltjes integral
for functions of bounded variation taking values in a Banach algebra with identity regardless of the choice of points ξk ε [tk−1, tk].
References
G. P. Butsan, “Necessary and sufficient condition for the existence of the Stieltjes integral for functions of bounded variation,”Dokl. Akad. Nauk Ukr. SSR, Ser. A, No. 12, 3–6 (1984).
A. N. Kolmogorov and S. V. Fomin,Elements of Function Theory and Functional Analysis [in Russian], Nauka, Moscow (1972).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 432–435, March, 1995.
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Karataeva, T.V. On the existence of the Stieltjes integral for functions of bounded variation. Ukr Math J 47, 504–508 (1995). https://doi.org/10.1007/BF01056317
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DOI: https://doi.org/10.1007/BF01056317