| Title:
|
Another Perron type integration in $n$ dimensions as an extension of integration of stepfunctions (English) |
| Author:
|
Jarník, Jiří |
| Author:
|
Kurzweil, Jaroslav |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
47 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
557-575 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
For a new Perron-type integral a concept of convergence is introduced such that the limit $f$ of a sequence of integrable functions $f_k$, $ k \in \mathbb N$ is integrable and any integrable $f$ is the limit of a sequence of stepfunctions $g_k$, $ k \in \mathbb N$. (English) |
| MSC:
|
26A39 |
| MSC:
|
26B99 |
| idZBL:
|
Zbl 0902.26006 |
| idMR:
|
MR1461432 |
| . |
| Date available:
|
2009-09-24T10:08:17Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127377 |
| . |
| Reference:
|
[1] J. Kurzweil and J. Jarník: Perron-type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence.Czechosl. Math. J. 46 (121) (1996), 1–20. MR 1371683 |
| Reference:
|
[2] J. Jarník and J. Kurzweil: Perron-type integration on $n$-dimensional intervals and its properties.Czechosl. Math. J. 45 (1995), 79–106. MR 1314532 |
| Reference:
|
[3] J. Kurzweil: Nichtabsolut konvergente Integrale.Teubner, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[4] E. J. McShane: A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals.Mem. Amer. Math. Soc. 88 (1969), . Zbl 0188.35702, MR 0265527 |
| Reference:
|
[5] J. Mawhin: Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields.Czechosl. Math. J. 31 (1981), 614–632. Zbl 0562.26004, MR 0631606 |
| Reference:
|
[6] E. J. McShane: Unified Integration.Academic Press, 1983. Zbl 0551.28001, MR 0740710 |
| . |
