The limit set of the Henstock-Kurzweil integral sums of a vector-valued function

  • A. G. Kostianko V.N.Karazin Kharkiv National University
Keywords: Henstock-Kurzweil integral, Banach space, limit set of integral sums

Abstract

We introduce the notion of the limit set $I_{H-K}(f)$ of the Henstock-Kurzweil integral sums of a function $f: [0, 1]\to X$, where $X$ is a Banach space, and study its properties. In particular, we construct an example of function $f$, which is not integrable, but its limit set consists exactly of one point. We find sufficient conditions that guarantee the convexity of the limit set.

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Author Biography

A. G. Kostianko, V.N.Karazin Kharkiv National University

References

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Published
2013-11-08
Cited
How to Cite
Kostianko, A. G. (2013). The limit set of the Henstock-Kurzweil integral sums of a vector-valued function. Visnyk of V. N. Karazin Kharkiv National University. Ser. Mathematics, Applied Mathematics and Mechanics, (1081), 10-20. https://doi.org/10.26565/2221-5646-2013-1081-02
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