| Title:
|
The AP-Denjoy and AP-Henstock integrals revisited (English) |
| Author:
|
Skvortsov, Valentin A. |
| Author:
|
Sworowski, Piotr |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
62 |
| Issue:
|
3 |
| Year:
|
2012 |
| Pages:
|
581-591 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The note is related to a recently published paper J. M. Park, J. J. Oh, C.-G. Park, D. H. Lee: The AP-Denjoy and AP-Henstock integrals. Czech. Math. J. 57 (2007), 689–696, which concerns a descriptive characterization of the approximate Kurzweil-Henstock integral. We bring to attention known results which are stronger than those contained in the aforementioned work. We show that some of them can be formulated in terms of a derivation basis defined by a local system of which the approximate basis is known to be a particular case. We also consider the relation between the $\sigma $-finiteness of variational measure generated by a function and the classical notion of the generalized bounded variation. (English) |
| Keyword:
|
approximate Kurzweil-Henstock integral |
| Keyword:
|
approximate continuity |
| Keyword:
|
local system |
| Keyword:
|
variational measure |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| MSC:
|
26A46 |
| idZBL:
|
Zbl 1265.26019 |
| idMR:
|
MR2984620 |
| DOI:
|
10.1007/s10587-012-0050-5 |
| . |
| Date available:
|
2012-11-10T20:57:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/143010 |
| . |
| Reference:
|
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| Reference:
|
[2] Bongiorno, D., Piazza, L. Di, Skvortsov, V. A.: Variational measures related to local systems and the Ward property of $\mathcal P$-adic path bases.Czech. Math. J. 56(131) (2006), 559-578. MR 2291756, 10.1007/s10587-006-0037-1 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
|
[7] Park, J. M., Oh, J. J., Kim, J., Lee, H. K.: The equivalence of the {AP}-Henstock and {AP}-Denjoy integrals.J. Chungcheong Math. Soc. 17 (2004), 103-110. |
| Reference:
|
[8] Park, J. M., Kim, Y. K., Yoon, J. H.: Some properties of the {AP}-Denjoy integral.Bull. Korean Math. Soc. 42 (2005), 535-541. Zbl 1090.26002, MR 2162209, 10.4134/BKMS.2005.42.3.535 |
| Reference:
|
[9] Park, J. M., Oh, J. J., Park, C.-G., Lee, D. H.: The {AP}-Denjoy and {AP}-Henstock integrals.Czech. Math. J. 57(132) (2007), 689-696. Zbl 1174.26308, MR 2337623, 10.1007/s10587-007-0106-0 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| . |
