| 摘要: |
| 本文研究Henstock-Kurzweil可积（HK可积）函数空间中的一个经典问题.文章通过研究分布Henstock-Kurzweil积分（DHK积分）的性质，给出了该问题的否定答案.进一步，利用收敛性获得了函数HK可积的一个充分必要条件.最后，在上述结论的基础上刻画了HK可积函数空间的紧性.所得结果丰富和推广了HK可积函数空间理论. |
| 关键词: Henstock-Kurzweil积分 分布导数 分布Henstock-Kurzweil积分 收敛定理 紧性 |
| DOI： |
| 分类号:O177.8 |
| 基金项目:Supported by the Fundamental Research Funds for the Central Universities (2019B44914); Natural Science Foundation of Jiangsu Province (BK20180500); the National Key Research and Development Program of China (2018YFC1508100). |
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| ON THE CHARACTERIZATION OF COMPACTNESS IN THE SPACE OF HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS |
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GUO Ya-ting1, YE Guo-ju1, LIU Wei1, ZHAO Da-fang2
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1.College of Science, Hohai University, Nanjing 210098, China;2.School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China
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| Abstract: |
| In this paper, we are concerned with a classical question in the space of HenstockKurzweil (shortly HK) integrable functions. A negative answer to this question is given by using the theory of the distributional Henstock-Kurzweil (shortly DHK) integral. Furthermore, we use convergence to prove a sufficient and necessary condition for a function to be HK integral and then give a characterization of compactness in the space of the HK integrable functions. The results enrich and extend the theory of HK integrable functions space. |
| Key words: Henstock-Kurzweil integral distributional derivative distributional HenstockKurzweil integral convergence theorem compactness |
