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The general gould type integral with respect to a multisubmeasure

In two earlier papers [GAVRILUŢ, A.: A Gould type integral with respect to a multisubmeasure, Math. Slovaca 58 (2008), 1–20] and [Gavriluţ, A.: On some properties of the Gould type integral with respect to a multisubmeasure, An. Ştiinţ. Univ. Al. I. Cuza Iaşi. Mat. (N.S.) 52 (2006), 177–194], we defined and studied a Gould type integral for a real valued, bounded function with respect to a multisubmeasure having finite variation. In this paper, we introduce and study the properties of a Gould type integral in the general setting: the function may be unbounded and the variation of the multisubmeasure may be infinite.