| Title:
|
On the Kluvánek Construction of the Lebesgue Integral (English) |
| Author:
|
Riečan, Beloslav |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2013 |
| Pages:
|
99-105 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
I. Kluvánek suggested to built the Lebesgue integral on a compact interval in the real line by the help of the length of intervals only. In the paper a modification of the Kluvánek construction is presented applicable to abstract spaces, too. (English) |
| Keyword:
|
Lebesgue integral |
| Keyword:
|
rings of sets |
| Keyword:
|
measures on compact interval |
| MSC:
|
28A25 |
| idZBL:
|
Zbl 06296018 |
| idMR:
|
MR3202383 |
| . |
| Date available:
|
2013-12-18T15:25:09Z |
| Last updated:
|
2014-07-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143542 |
| . |
| Reference:
|
[1] Boccuto A., Riečan B., Vrábelová M.: Kurzweil–Henstock Integral in Riesz Spaces. Betham, 2009. |
| Reference:
|
[2] Kluvánek, I.: Archimedes was right. Elemente der Mathematik 42, 3 (1987), 51–82. Zbl 0706.26005, MR 0886766 |
| Reference:
|
[3] Kluvánek, I.: Archimedes was right. Elemente der Mathematik 42, 4 (1987), 83–114. Zbl 0706.26005, MR 0896118 |
| Reference:
|
[4] Kluvánek, I.: Integral Calculus. UK, Ružomberok, 2011 (in Slovak). |
| Reference:
|
[5] Riečan, B.: On Probability and Measure. Alfa, Bratislava, 1971 (in Slovak). |
| Reference:
|
[6] Riečan, B., Neubrunn T.: Integral, Measure, and Ordering. Kluwer, Dordrecht, 1997. Zbl 0916.28001, MR 1489521 |
| Reference:
|
[7] Riečan, B., Tkáčik, Š.: A note on the Kluvánek integral. Tatra Mt. Math. Publ 49 (2011), 59–65. Zbl 1265.26018, MR 2865796 |
| Reference:
|
[8] Šipoš, J.: Integral representation of nonlinear functionals. Math. Slovaca 29 (1979), 333–346. MR 0562006 |
| . |
