In this paper we introduce and develop an integration theory of a real-valued function with respect to a strongly bounded and finitely additive set function m with values in a locally convex topological vector space (LCTVS) X, using both a weak and a strong approach. Then we investigate the relationships among these two integrals; in particular, assuming the sequential completeness of X, the separability of the range of m and a form of Lebesgue integrability on [0,∞) by seminorms of the distribution functions we prove that all the integrals coincide. Finally we show the above integrals can be considered as Burkill-Cesari integrals.
On integration with respect to LCTVS-valued finitely additive measures
MARTELLOTTI, Anna
1994
Abstract
In this paper we introduce and develop an integration theory of a real-valued function with respect to a strongly bounded and finitely additive set function m with values in a locally convex topological vector space (LCTVS) X, using both a weak and a strong approach. Then we investigate the relationships among these two integrals; in particular, assuming the sequential completeness of X, the separability of the range of m and a form of Lebesgue integrability on [0,∞) by seminorms of the distribution functions we prove that all the integrals coincide. Finally we show the above integrals can be considered as Burkill-Cesari integrals.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
