2019
Том 71
№ 11

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On the existence of the Stieltjes integral for functions of bounded variation

Karataeva T. V.

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Abstract

We obtain sufficient conditions of existence of the Stieltjes integral $$\int\limits_s^t {f(\tau )} d\mathcal{F}(\tau ) = \mathop {\lim }\limits_{\delta _n \to 0} \sum\limits_{k = 1}^{m_n } {f(\xi _k )(\mathcal{F}(t_k^n ) - \mathcal{F}(t_{k - 1}^n ))}$$ for functions of bounded variation taking values in a Banach algebra with identity regardless of the choice of points $ξ_k \in [t_{k−1}, t_k]$.

English version (Springer): Ukrainian Mathematical Journal 47 (1995), no. 3, pp 504–508.

Citation Example: Karataeva T. V. On the existence of the Stieltjes integral for functions of bounded variation // Ukr. Mat. Zh. - 1995. - 47, № 3. - pp. 432-435.

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