Bongiorno, Benedetto Relatively weakly compact sets in the Denjoy space. (English) Zbl 1045.26502 J. Math. Study 27, No. 1, 37-44 (1994). By the “Denjoy space” the author means the space \(H\) of all Henstock-Kurzweil integrable functions on a compact interval \(I :=[a,b]\) of \(\mathbb{R}\), equipped with the seminorm \(| f| := \sup\{|\int_a^xf|:x\in I\}\). The author finds necessary and sufficient conditions for a subset of \(H\) (and of its completion) to be relatively weakly compact. The conditions involve (i) boundedness, (ii) equicontinuity on a dense subset of \(I\) and (iii) an “asymptotic \(ACG^*\)-condition”. Reviewer: R. G. Bartle (MR 95i:00035) Cited in 11 Documents MSC: 26A39 Denjoy and Perron integrals, other special integrals 46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) Keywords:Denjoy spaces; Henstock-Kurzweil integral PDFBibTeX XMLCite \textit{B. Bongiorno}, J. Math. Study 27, No. 1, 37--44 (1994; Zbl 1045.26502)