We introduce and investigate a Henstock-Kurzweil-type integral for Riesz space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypotheses the generalized Riemann integral and that every simple function vanishing outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one.
On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
BOCCUTO, Antonio;
2004
Abstract
We introduce and investigate a Henstock-Kurzweil-type integral for Riesz space-valued functions defined on (not necessarily bounded) subintervals of the extended real line. We prove some basic properties, among them the fact that our integral contains under suitable hypotheses the generalized Riemann integral and that every simple function vanishing outside of a set of finite Lebesgue measure is integrable according to our definition, and in this case our integral coincides with the usual one.File in questo prodotto:
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