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 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 
@article{CMJ_2004_54_3_a4,
     author = {Boccuto, A. and Rie\v{c}an, B.},
     title = {On the {Henstock-Kurzweil} integral for {Riesz-space-valued} functions defined on unbounded intervals},
     journal = {Czechoslovak Mathematical Journal},
     pages = {591--607},
     year = {2004},
     volume = {54},
     number = {3},
     mrnumber = {2086719},
     zbl = {1080.28007},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a4/}
}
TY  - JOUR
AU  - Boccuto, A.
AU  - Riečan, B.
TI  - On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
JO  - Czechoslovak Mathematical Journal
PY  - 2004
SP  - 591
EP  - 607
VL  - 54
IS  - 3
UR  - http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a4/
LA  - en
ID  - CMJ_2004_54_3_a4
ER  - 
%0 Journal Article
%A Boccuto, A.
%A Riečan, B.
%T On the Henstock-Kurzweil integral for Riesz-space-valued functions defined on unbounded intervals
%J Czechoslovak Mathematical Journal
%D 2004
%P 591-607
%V 54
%N 3
%U http://geodesic.mathdoc.fr/item/CMJ_2004_54_3_a4/
%G en
%F CMJ_2004_54_3_a4
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/