| Title:
|
The Kurzweil construction of an integral in ordered spaces (English) |
| Author:
|
Riečan, Beloslav |
| Author:
|
Vrábelová, Marta |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
48 |
| Issue:
|
3 |
| Year:
|
1998 |
| Pages:
|
565-574 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This paper generalizes the results of papers which deal with the Kurzweil-Henstock construction of an integral in ordered spaces. The definition is given and some limit theorems for the integral of ordered group valued functions defined on a Hausdorff compact topological space $T$ with respect to an ordered group valued measure are proved in this paper. (English) |
| Keyword:
|
lattice ordered group valued function and measure |
| Keyword:
|
Kurzweil-Henstock construction of an integral |
| Keyword:
|
limit theorems |
| MSC:
|
26A39 |
| MSC:
|
28B15 |
| idZBL:
|
Zbl 0953.28007 |
| idMR:
|
MR1637875 |
| . |
| Date available:
|
2009-09-24T10:15:54Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127436 |
| . |
| Reference:
|
[1] Boccuto, A.: Riesz spaces, integration and sandwich theorems.Tatra Mountains Math. Publ. 3 (1993), 213–230. Zbl 0815.28007, MR 1278536 |
| Reference:
|
[2] Duchoň, M. – Riečan, B.: On the Kurzweil-Stieltjes integral in ordered spaces.Tatra Mountains Math. Publ 8 (1996), 133–141. MR 1475272 |
| Reference:
|
[3] Haluška, J.: On integration in complete vector lattices.Tatra Mountains Math. Publ. 3 (1993), 201–212. MR 1278535 |
| Reference:
|
[4] Henstock, R.: The General Theory of Integration.Oxford, 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
|
[5] Kurzweil, J.: Nicht absolut konvergente Integrale.Teubner Leipzig, 1980. MR 0597703 |
| Reference:
|
[6] Riečan, B.: On the Kurzweil integral in compact topological spaces.Rad. Mat. 2 (1986), 151–163. MR 0873695 |
| Reference:
|
[7] Riečan, B.: On the Kurzweil integral for functions with values in ordered spaces I.Acta Math. Univ. Comeniana 56–57 (1990), 75–83. MR 1083014 |
| Reference:
|
[8] Riečan, B. – Vrábelová, M.: On the Kurzweil integral for functions with values in ordered spaces II.Math. Slov. 43 (1993), 471–475. MR 1248980 |
| Reference:
|
[9] Riečan, B. – Vrábelová, M.: On integration with respect to operator valued measures in Riesz spaces.Tatra Mountains Math. Publ. 2 (1993), 149–165. MR 1251049 |
| Reference:
|
[10] Száz, A.: The fundamental theorem of calculus in an abstract setting.Tatra Mountains Math. Publ. 2 (1993), 167–174. MR 1251050 |
| Reference:
|
[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. MR 1475267 |
| . |
