A particular notion of limit is introduced, for Riesz space valued functions. The definition is related to a suitable ideal of the domain, and includes the so-called stochastic convergence. It is shown that every extended real valued function admits limit, and this in turn gives extensions of finitely additive measures. The results are then generalized to Riesz space-valued functions, in a suitable form.
Defining Limits by means of Integrals
BOCCUTO, Antonio;CANDELORO, Domenico
2009
Abstract
A particular notion of limit is introduced, for Riesz space valued functions. The definition is related to a suitable ideal of the domain, and includes the so-called stochastic convergence. It is shown that every extended real valued function admits limit, and this in turn gives extensions of finitely additive measures. The results are then generalized to Riesz space-valued functions, in a suitable form.File in questo prodotto:
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