×

The Kurzweil construction of an integral in ordered spaces. (English) Zbl 0953.28007

For functions and regular measures with values in abstract Abelian lattice ordered groups the Kurzweil type integral over a Hausdorff compact topological space is introduced and it is shown that some of the usual convergence theorems can be proved in this abstract setting.

MSC:

28B15 Set functions, measures and integrals with values in ordered spaces
26A39 Denjoy and Perron integrals, other special integrals
PDFBibTeX XMLCite
Full Text: DOI EuDML

References:

[1] Boccuto, A.: Riesz spaces, integration and sandwich theorems. Tatra Mountains Math. Publ. 3 (1993), 213-230. · Zbl 0815.28007
[2] Duchoň, M. - Riečan, B.: On the Kurzweil-Stieltjes integral in ordered spaces. Tatra Mountains Math. Publ 8 (1996), 133-141. · Zbl 0918.28013
[3] Haluška, J.: On integration in complete vector lattices. Tatra Mountains Math. Publ. 3 (1993), 201-212. · Zbl 0813.46035
[4] Henstock, R.: The General Theory of Integration. Oxford, 1991. · Zbl 0745.26006
[5] Kurzweil, J.: Nicht absolut konvergente Integrale. Teubner Leipzig, 1980. · Zbl 0441.28001
[6] Riečan, B.: On the Kurzweil integral in compact topological spaces. Rad. Mat. 2 (1986), 151-163. · Zbl 0623.28003
[7] Riečan, B.: On the Kurzweil integral for functions with values in ordered spaces I. Acta Math. Univ. Comeniana 56-57 (1990), 75-83. · Zbl 0735.28008
[8] Riečan, B. - Vrábelová, M.: On the Kurzweil integral for functions with values in ordered spaces II. Math. Slov. 43 (1993), 471-475. · Zbl 0821.28007
[9] Riečan, B. - Vrábelová, M.: On integration with respect to operator valued measures in Riesz spaces. Tatra Mountains Math. Publ. 2 (1993), 149-165. · Zbl 0797.28008
[10] Száz, A.: The fundamental theorem of calculus in an abstract setting. Tatra Mountains Math. Publ. 2 (1993), 167-174. · Zbl 0796.28004
[11] Vrábelová, M. - Riečan, B.: On the Kurzweil integral for functions with values in ordered spaces III. Tatra Mountains Math. Publ 8 (1996), 93-100. · Zbl 0918.28012
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.