Xu, Dongfu; Lee, Tuo-Yeong; Lee, Peng-Yee On some integration by parts formulae for the APS-integral. (English) Zbl 0926.26005 J. Math. Study 27, No. 1, 181-184 (1994). Summary: The main results of this paper are as follows:Let \(F\) be approximately continuous on \([a,b]\) and \(g\) be of bounded variation on \([a,b]\). Then (APS) \(\int^b_a F dg\) exists if and only if (APS) \(\int^b_a g dF\) exists. Furthermore, suppose (APS) \(\int^b_a F dy\) or (APS) \(\int^b_a g dF\) exists, then we have \[ (\text{APS})\;\int^b_a F dg+ (\text{APS})\;\int^b_a g dF= F(b)g(b)- F(a)g(a). \] MSC: 26A39 Denjoy and Perron integrals, other special integrals Keywords:AP-Stieltjes integral; approximate full cover; AFC; integration by parts formulae; APS-integral; approximately continuous Perron integral; \(\text{ACG}^*_{ap}\) PDFBibTeX XMLCite \textit{D. Xu} et al., J. Math. Study 27, No. 1, 181--184 (1994; Zbl 0926.26005)