In this note we define three variations for a vector valued function defined on an inf-semilattice, all of them generalizations of those considered for vector valued set-functions. We are interested in additive and finiteness properties of such variations.
The Girsanov's theorem is useful as well in the general theory of stochastic analysis as well in its applications. We show here that it can be also applied to the theory of stochastic differential inclusions. In particular, we obtain some special properties of sets of weak solutions to some type of these inclusions.
We present some convergence theorems for the HK-integral of functions taking values in a locally convex space. These theorems are based on the concept of HK-equiintegrability.
In this paper we examine the set of weakly continuous solutions for a Volterra integral equation in Henstock-Kurzweil-Pettis integrability settings. Our result extends those obtained in several kinds of integrability settings. Besides, we prove some new fixed point theorems for function spaces relative to the weak topology which are basic in our considerations and comprise the theory of differential and integral equations in Banach spaces.
In this paper we present some new versions of Brooks-Jewett and Dieudonné-type theorems for -group-valued measures.
Nell'ultimo ventennio tutta una serie di lavori è stata rivolta allo studio delle misure su strutture algebriche più generali delle algebre di Boole, come i poset e i reticoli ortomodulari, le effect algebras, le BCK-algebras. La teoria così ottenuta interessa l'analisi funzionale, il calcolo delle probabilità e la topologia, più recentemente la teoria delle decisioni. Si presentano alcuni risultati relativi a misure su strutture algebriche non-standard analizzando, in particolare, gli aspetti topologici...
We present the full descriptive characterizations of the strong McShane integral (or the variational McShane integral) of a Banach space valued function defined on a non-degenerate closed subinterval of in terms of strong absolute continuity or, equivalently, in terms of McShane variational measure generated by the primitive of , where is the family of all closed non-degenerate subintervals of .
Some limit and Dieudonné-type theorems in the setting of (ℓ)-groups with respect to filter convergence are proved, extending earlier results.
Let be a completely regular Hausdorff space, the space of all scalar-valued bounded continuous functions on with strict topologies. We prove that these are locally convex topological algebras with jointly continuous multiplication. Also we find the necessary and sufficient conditions for these algebras to be locally -convex.