We introduce here a version of KH-integral for two-variable functions with values in metric semigroups. We obtain for it convergence results and a version of the Fubini Theorem. In this paper we introduce the two dimensional Kurzweil-Henstock integral for metric semigroup-valued functions, defined in (not necessarily bounded) subrectangles of the extended Cartesian plane. We prove for it convergence results both with respect to sequences of functions (convergence theorems related with equiintegrability), and with respect to increasing families of sets (the Hake theorem). Moreover, following a line of research on double integration in the context of Riesz spaces, we give also a version of the Fubini theorem which generalizes a similar result for mappings defined in a compact subrectangle of R^2.
Convergence and Fubini Theorems for metric semigroup-valued functions defined on unbounded rectangles
BOCCUTO, Antonio;SAMBUCINI, Anna Rita
2009
Abstract
We introduce here a version of KH-integral for two-variable functions with values in metric semigroups. We obtain for it convergence results and a version of the Fubini Theorem. In this paper we introduce the two dimensional Kurzweil-Henstock integral for metric semigroup-valued functions, defined in (not necessarily bounded) subrectangles of the extended Cartesian plane. We prove for it convergence results both with respect to sequences of functions (convergence theorems related with equiintegrability), and with respect to increasing families of sets (the Hake theorem). Moreover, following a line of research on double integration in the context of Riesz spaces, we give also a version of the Fubini theorem which generalizes a similar result for mappings defined in a compact subrectangle of R^2.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
