Guo, Yating; Ye, Guoju; Liu, Wei; Zhao, Dafang On the characterization of compactness in the space of Henstock-Kurzweil integrable functions. (English) Zbl 1474.26032 J. Math., Wuhan Univ. 41, No. 1, 12-24 (2021). Summary: 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 \({D_{HK}}\)) 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. MSC: 26A39 Denjoy and Perron integrals, other special integrals 46F10 Operations with distributions and generalized functions 46G12 Measures and integration on abstract linear spaces Keywords:Henstock-Kurzweil integral; distributional derivative; distributional Henstock-Kurzweil integral; convergence theorem; compactness PDFBibTeX XMLCite \textit{Y. Guo} et al., J. Math., Wuhan Univ. 41, No. 1, 12--24 (2021; Zbl 1474.26032) Full Text: DOI