| Title:
|
Perron type integration on $n$-dimensional intervals as an extension of integration of stepfunctions by strong equiconvergence (English) |
| Author:
|
Kurzweil, Jaroslav |
| Author:
|
Jarník, Jiří |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
1996 |
| Pages:
|
1-20 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A39 |
| MSC:
|
26B15 |
| MSC:
|
26B99 |
| idZBL:
|
Zbl 0902.26007 |
| idMR:
|
MR1371683 |
| DOI:
|
10.21136/CMJ.1996.127265 |
| . |
| Date available:
|
2009-09-24T09:52:58Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127265 |
| . |
| Reference:
|
[1] R. A. Gordon: A general convergence theorem for nonabsolute integrals.J. London Math. Soc. 44 (1991), 301–309. Zbl 0746.26003, MR 1136442 |
| Reference:
|
[2] R. A. Gordon: On the equivalence of two convergence theorems for the Henstock integral.Real Anal. Exchange 18 (1992/93), 261–266. MR 1205521 |
| Reference:
|
[3] 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:
|
[4] J. Kurzweil and J. Jarník: Differentiability and integrability in $n$ dimensions with respect to $\alpha $-regular intervals.Results in Mathematik 21 (1992), 138–151. MR 1146639, 10.1007/BF03323075 |
| Reference:
|
[5] J. Jarník, J. Kurzweil and Š. Schwabik: On Mawhin’s approach to multiple nonabsolutely convergent integrals.Čas. pěst. mat. 108 (1983), 356–380. MR 0727536 |
| Reference:
|
[6] P. Y. Lee and T. S. Chew: A better convergence theorem for Henstock integrals.Bull. London Math. Soc. 17 (1985), 557–564. MR 0813739, 10.1112/blms/17.6.557 |
| Reference:
|
[7] P. Y. Lee and T. S. Chew: A Riesz-type definition of the Denjoy integral.Real Anal. Exchange 11 (1985/86), 221–227. MR 0828492 |
| Reference:
|
[8] E. J. McShane: Integration.Princeton University Press, 1947. Zbl 0033.05302, MR 0082536 |
| Reference:
|
[9] F. Riesz and B. Sz. Nagy: Vorlesungen über Funktionalanalysis.VEB Deutscher Verlag der Wissenschaften Berlin, 1956. MR 0083695 |
| Reference:
|
[10] K. Yosida: Functional Analysis.Springer-Verlag, Berlin-Göttingen-Heidelberg, 1965. Zbl 0126.11504 |
| . |
