| Henstock-Kurzweil可积函数空间的紧性特征 |
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| 引用本文： | 郭雅婷,叶国菊,刘尉,赵大方.Henstock-Kurzweil可积函数空间的紧性特征[J].数学杂志,2021(1):12-24. |
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| 作者姓名： | 郭雅婷 叶国菊 刘尉 赵大方 |
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| 作者单位： | 河海大学理学院;湖北师范大学数学与统计学院 |
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| 基金项目： | 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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| 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.
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| 关 键 词： | Henstock-Kurzweil积分 分布导数 分布Henstock-Kurzweil积分 收敛定理 紧性 |
ON THE CHARACTERIZATION OF COMPACTNESS IN THE SPACE OF HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS |
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| GUO Ya-ting,YE Guo-ju,LIU Wei,ZHAO Da-fang.ON THE CHARACTERIZATION OF COMPACTNESS IN THE SPACE OF HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS[J].Journal of Mathematics,2021(1):12-24. |
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| Authors: | GUO Ya-ting YE Guo-ju LIU Wei ZHAO Da-fang |
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| Institution: | (College of Science,Hohai University,Nanjing 210098,China;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 Henstock-Kurzweil(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. |
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| Keywords: | Henstock-Kurzweil integral distributional derivative distributional Henstock-Kurzweil integral convergence theorem compactness |
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