Here, we consider abstract structures, similar to the so-called "convergence-groups", which were introduced by Fischer. Other types of "abstract" spaces were investigated also by Avallone and Basile , Kusraev and Malyugin , Nakanishi and others. In this paper an integral is dened, for R1-valued functions, defined on an arbitrary set X; with respect to a R2-valued (finitely additive) mean and R1 and R2are convergence groups, "linked together" by some kind of bilinear mappings. Our integral will be an element of another convergence group R. The results here obtained extend both the cases of Riesz spaces (see [3]) and of topological groups.Finally, we give a comparison with some classical integrals, like Bochner, Pettis and stochastic integral.
Abstract integration in convergence groups
BOCCUTO, Antonio;SAMBUCINI, Anna Rita
1998
Abstract
Here, we consider abstract structures, similar to the so-called "convergence-groups", which were introduced by Fischer. Other types of "abstract" spaces were investigated also by Avallone and Basile , Kusraev and Malyugin , Nakanishi and others. In this paper an integral is dened, for R1-valued functions, defined on an arbitrary set X; with respect to a R2-valued (finitely additive) mean and R1 and R2are convergence groups, "linked together" by some kind of bilinear mappings. Our integral will be an element of another convergence group R. The results here obtained extend both the cases of Riesz spaces (see [3]) and of topological groups.Finally, we give a comparison with some classical integrals, like Bochner, Pettis and stochastic integral.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
