Henstock-Kurzweil可积函数空间的紧性特征  

ON THE CHARACTERIZATION OF COMPACTNESS IN THE SPACE OF HENSTOCK-KURZWEIL INTEGRABLE FUNCTIONS

作　　者：郭雅婷 叶国菊[1] 刘尉[1] 赵大方 GUO Ya-ting;YE Guo-ju;LIU Wei;ZHAO Da-fang(College of Science,Hohai University,Nanjing 210098,China;School of Mathematics and Statistics,Hubei Normal University,Huangshi 435002,China)

机构地区：[1]河海大学理学院,江苏南京210098 [2]湖北师范大学数学与统计学院,湖北黄石435002

出　　处：《数学杂志》2021年第1期12-24,共13页Journal of Mathematics

基　　金：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).

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.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.

关 键 词：Henstock-Kurzweil积分 分布导数 分布Henstock-Kurzweil积分 收敛定理 紧性 

分 类 号：O177.8[理学—基础数学]