| Title:
|
On McShane-type integrals with respect to some derivation bases (English) |
| Author:
|
Skvortsov, Valentin A. |
| Author:
|
Sworowski, Piotr |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
131 |
| Issue:
|
4 |
| Year:
|
2006 |
| Pages:
|
365-378 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some observations concerning McShane type integrals are collected. In particular, a simple construction of continuous major/minor functions for a McShane integrand in $\mathbb{R}^n$ is given. (English) |
| Keyword:
|
McShane integral |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
Perron integral |
| Keyword:
|
basis |
| MSC:
|
26A39 |
| idZBL:
|
Zbl 1112.26010 |
| idMR:
|
MR2273928 |
| DOI:
|
10.21136/MB.2006.133973 |
| . |
| Date available:
|
2009-09-24T22:27:25Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133973 |
| . |
| Reference:
|
[1] Bongiorno, B., Di Piazza, L., Skvortsov, V.: On the $n$-dimensional Perron integral defined by ordinary derivates.Real Anal. Exchange 26 (2000/01), 371–380. MR 1825515 |
| Reference:
|
[2] Bongiorno, B., Di Piazza, L., Skvortsov, V.: On dyadic integrals and some other integrals associated with local systems.J. Math. Anal. Appl. 271 (2002), 506–524. MR 1923649, 10.1016/S0022-247X(02)00146-4 |
| Reference:
|
[3] Bongiorno, B., Di Piazza, L., Skvortsov, V.: The Ward property for a ${\mathcal{P}}$-adic basis and the ${\mathcal{P}}$-adic integral.J. Math. Anal. Appl. 285 (2003), 578–592. MR 2005142, 10.1016/S0022-247X(03)00426-8 |
| Reference:
|
[4] Filipczak, T.: Intersection conditions for some density and ${\mathcal{I}}$-density local systems.Real Anal. Exchange 15 (1989/90), 170–192. MR 1042535, 10.2307/44151997 |
| Reference:
|
[5] Gordon, R. A.: The inversion of approximate and dyadic derivatives using an extension of the Henstock integral.Real Anal. Exchange 16 (1990/91), 154–168. MR 1087481 |
| Reference:
|
[6] Gordon, R. A.: Review of [7].Math. Reviews 2005d:26011. |
| Reference:
|
[7] Kim, J. B., Lee, D. H., Lee, W. Y., Park, C. G., Park, J. M.: The s-Perron, sap-Perron and ap-McShane integrals.Czechoslovak Math. J. 54 (2004), 545–557. MR 2086715, 10.1007/s10587-004-6407-7 |
| Reference:
|
[8] Pfeffer, W. F.: The Riemann Approach to Integration.Cambridge University Press, Cambridge, 1993. Zbl 0804.26005, MR 1268404 |
| Reference:
|
[9] Skvortsov, V.: Continuity of $\delta $-variation and construction of continuous major and minor functions for the Perron integral.Real Anal. Exchange 21 (1995/96), 270–277. MR 1377536 |
| Reference:
|
[10] Thomson, B. S.: Real Functions.Lecture Notes in Mathematics, vol. 1170, Springer, 1985. Zbl 0581.26001, MR 0818744 |
| Reference:
|
[11] Thomson, B. S.: Symmetric Properties of Real Functions.Monographs and Textbooks in Pure and Applied Mathematics, vol. 183, Marcel Dekker, New York, 1994. Zbl 0809.26001, MR 1289417 |
| Reference:
|
[12] Wang, C., Ding, C. S.: An integral involving Thomson’s local systems.Real Anal. Exchange 19 (1993/94), 248–253. MR 1268851 |
| . |
