In this paper we construct an integration theory for finitely additive measures defined on an algebra with values in a Banach space. We use two different approaches to define the integration theory, one of which is an extension of the de Giorgi-Letta integral defined for monotone set functions. Our extension of their theory reduces integration in the above-mentioned setting to the study of the Bochner integral on the real line, where the set function is either the semivariation or the norm of the Banach-space-valued measure. This theory complements the infinite-dimensional bilinear integral developed by Brooks and Dinculeanu, in which the main emphasis was on integration with respect to a family of Banach-space-valued measures.
On the De Giorgi-Letta integral in infinite dimensions
MARTELLOTTI, Anna
1991
Abstract
In this paper we construct an integration theory for finitely additive measures defined on an algebra with values in a Banach space. We use two different approaches to define the integration theory, one of which is an extension of the de Giorgi-Letta integral defined for monotone set functions. Our extension of their theory reduces integration in the above-mentioned setting to the study of the Bochner integral on the real line, where the set function is either the semivariation or the norm of the Banach-space-valued measure. This theory complements the infinite-dimensional bilinear integral developed by Brooks and Dinculeanu, in which the main emphasis was on integration with respect to a family of Banach-space-valued measures.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
