Volčič, Aljoša A Riemann-type theorem for a Riemann-type integral. (English) Zbl 1429.26011 Ric. Mat. 68, No. 2, 333-339 (2019). Summary: For functions which are Henstock-Kurzweil integrable but not Lebesgue-integrable we prove a theorem which resembles the Riemann theorem on the rearrangement of conditionally convergent series. MSC: 26A39 Denjoy and Perron integrals, other special integrals 40A10 Convergence and divergence of integrals Keywords:rearrangement; Henstock-Kurzweil integral; Fubini-Tonelli theorem PDFBibTeX XMLCite \textit{A. Volčič}, Ric. Mat. 68, No. 2, 333--339 (2019; Zbl 1429.26011) Full Text: DOI References: [1] Henstock, R.: A problem in two-dimensional integration. J. Austral. Math. Soc. Ser. A 35(3), 386-404 (1983) · Zbl 0549.26007 · doi:10.1017/S1446788700027087 [2] Lee, T.Y.: Product variational measures and Fubini-Tonelli type theorems for the Henstock-Kurzweil integral. J. Math. Anal. Appl. 298, 677-692 (2004) · Zbl 1065.26013 · doi:10.1016/j.jmaa.2004.05.033 [3] Pfeffer, W.: The Riemann Approach to Integration. Cambridge University Press, Cambridge (1993) · Zbl 0804.26005 [4] Riemann, B.: Über die Darstellbarkeit einer Function durch eine trigonometrische Reihe. Abhandlungen der Königlichen Gesellschaft der Wissenschaften zu Göttingen, vol. 13 (1867) [5] Rao, G., Tulone, F.: Analogue of the Riemann-Dini theorem for non-absolutely convergent integrals. Le Matematiche, vol. LXII fasc. I, (2007) 129-134 · Zbl 1150.26004 [6] Rao, G., Tulone, F.: Henstock integral and Dini-Riemann theorem. Le Matematiche, vol. LXIV fasc. II, (2009) 71-77 · Zbl 1198.26015 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.