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On some integration by parts formulae for the APS-integral. (English) Zbl 0926.26005

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
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