| Title:
|
Convergence theorems for the Perron integral and Sklyarenko's condition (English) |
| Author:
|
Schwabik, Štefan |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
33 |
| Issue:
|
2 |
| Year:
|
1992 |
| Pages:
|
237-244 |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that a uniform version of Sklyarenko's integrability condition for Perron integrals together with pointwise convergence of a sequence of integrable functions are sufficient for a convergence theorem for Perron integrals. (English) |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
Perron integral |
| MSC:
|
26A39 |
| idZBL:
|
Zbl 0774.26004 |
| idMR:
|
MR1189654 |
| . |
| Date available:
|
2009-01-08T17:55:16Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118491 |
| . |
| Reference:
|
[1] Henstock R.: Lectures on the Theory of Integration.World Scientific Singapore (1988). Zbl 0668.28001, MR 0963249 |
| Reference:
|
[2] Henstock R.: The General Theory of Integration.Clarendon Press Oxford (1991). Zbl 0745.26006, MR 1134656 |
| Reference:
|
[3] Kurzweil J.: Nichtabsolut konvergente Integrale.BSB B.G. Teubner Verlagsgesellschaft Leipzig (1980). Zbl 0441.28001, MR 0597703 |
| Reference:
|
[4] Lee Peng-Yee: Lanzhou Lectures on Henstock Integration.World Scientific Singapore (1989). Zbl 0699.26004, MR 1050957 |
| Reference:
|
[5] Mawhin J.: Introduction à l'Analyse.CABAY, Libraire-éditeur Louvain-La-Neuve (1984). |
| Reference:
|
[6] McLeod R.M.: The Generalized Riemann Integral.Math. Assoc. of America (1980). Zbl 0486.26005, MR 0588510 |
| Reference:
|
[7] Preiss D., Schwabik Š.: The definite integral.Mimeographed notes in Czech Math.-Phys. Fac. of the Charles Univ. and Math. Inst. of the Czech. Acad. Sci Prague (1979), 138 pages. |
| Reference:
|
[8] Saks S.: Theory of the integral.Warszawa (1937). Zbl 0017.30004 |
| Reference:
|
[9] Sklyarenko V.A.: On integration by parts for Burkill's SCP-integral.Mat. Sbornik 630-646 (1980), 112. MR 0587041 |
| Reference:
|
[10] Thomson B.S.: Derivation bases on the real line (II).Real Analysis Exchange 8 278-442 (1982-83). Zbl 0525.26003, MR 0700194 |
| . |
