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A Gould type integral with respect to a multisubmeasure

In: Mathematica Slovaca, vol. 58, no. 1
Alina Cristiana Gavriluţ
Detaily:
Rok, strany: 2008, 43 - 62
Kľúčové slová:
Gould-integral, submeasure, multisubmeasure, multivalued Gould-integral
O článku:
In [GOULD, G. G.: \textit{Integration over vector-valued measures}, Proc. London Math. Soc. (3) \textbf{15}, (1965), 193–205], G. G. Gould introduced a type of integral of a bounded, real valued function with respect to a finite additive set function taking values in a Banach space, integral which is more general than the Lebesgue one. Recently, A. Precupanu and A. Croitoru gave the generalization, defining a Gould type integral for multimeasures with values in $\mathcal{P}kc(X)$, $X$ being a Banach space ([PRECUPANU, A.—CROITORU, A.: \textit{A Gould type integral with respect to a multimeasure, I}, An. \c{S}tiin\c{t}. Univ. ``Al. I. Cuza'' Ia\c{s}i Sec\c{t}. I a Mat. \textbf{48} (2002), 165–200]). Taking as starting point this work and [PRECUPANU, A.—CROITORU, A.: \textit{A Gould type integral with respect to a multimeasure, II}, An. \c{S}tiin\c{t}. Univ. ``Al. I. Cuza'' Ia\c{s}i Sec\c{t}. I a Mat. \textbf{49} (2003), 183–207], we define here the notion of a Gould type integral with respect to a $\mathcal{P}bf(X)$-valued multisubmeasure, pointing out important properties of it. We also establish that, even if we deal with multisubmeasures, the integral is still a multimeasure.
Ako citovať:
ISO 690:
Gavriluţ, A. 2008. A Gould type integral with respect to a multisubmeasure. In Mathematica Slovaca, vol. 58, no.1, pp. 43-62. 0139-9918.

APA:
Gavriluţ, A. (2008). A Gould type integral with respect to a multisubmeasure. Mathematica Slovaca, 58(1), 43-62. 0139-9918.