数学杂志2021，Vol.41Issue(1)：12-24,13.
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
摘要
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.关键词
Henstock-Kurzweil积分/分布导数/分布Henstock-Kurzweil积分/收敛定理/紧性Key words
Henstock-Kurzweil integral/distributional derivative/distributional Henstock-Kurzweil integral/convergence theorem/compactness分类
数理科学引用本文复制引用
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,2021,41(1):12-24,13.基金项目
Supported by the Fundamental Research Funds for the Central Universities(2019B44914) （2019B44914）
Natural Science Foundation of Jiangsu Province(BK20180500) （BK20180500）
the National Key Re-search and Development Program of China(2018YFC1508100). （2018YFC1508100）
