In order to study certain types of problems (for example stochastic integration and equations) it would be "natural" to consider spaces of extended real-valued functions. Sometimes it is advisable that the functions involved are continuous with respect to some suitable topologies, and endowed with an order structure. The "natural" context is that of Riesz space, which allows us to deal also with convergences, not generated by any topology. Some concepts of continuity and differentiability are introduced for Riesz space-valued maps. We develop a Kurzweil-Henstock-type integration theory for Riesz space-valued functions with respect to order convergence, and prove some versions of the Fundamental Formula of Calculus.
Differential and Integral Calculus in Riesz spaces
BOCCUTO, Antonio
1998
Abstract
In order to study certain types of problems (for example stochastic integration and equations) it would be "natural" to consider spaces of extended real-valued functions. Sometimes it is advisable that the functions involved are continuous with respect to some suitable topologies, and endowed with an order structure. The "natural" context is that of Riesz space, which allows us to deal also with convergences, not generated by any topology. Some concepts of continuity and differentiability are introduced for Riesz space-valued maps. We develop a Kurzweil-Henstock-type integration theory for Riesz space-valued functions with respect to order convergence, and prove some versions of the Fundamental Formula of Calculus.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
