Geodesic
On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 591-607
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In this paper 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 hypothesis the generalized Riemann integral and that every simple function which vanishes 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.
In this paper 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 hypothesis the generalized Riemann integral and that every simple function which vanishes 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.
Classification : 28B05, 28B10, 28B15, 46G10
Keywords: Riesz spaces; Henstock-Kurzweil integral 
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Boccuto, A.; Riečan, B. On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals. Czechoslovak Mathematical Journal, Tome 54 (2004) no. 3, pp. 591-607. http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a4/

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