| Title:
|
General integration and extensions.II (English) |
| Author:
|
Schwabik, Štefan |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
60 |
| Issue:
|
4 |
| Year:
|
2010 |
| Pages:
|
983-1005 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This work is a continuation of the paper (Š. Schwabik: General integration and extensions I, Czechoslovak Math.\ J. 60 (2010), 961--981). Two new general extensions are introduced and studied in the class $\frak T$ of general integrals. The new extensions lead to approximate description of the Kurzweil-Henstock integral based on the Lebesgue integral close to the results of S. Nakanishi presented in the paper (S. Nakanishi: A new definition of the Denjoy's special integral by the method of successive approximation, Math.\ Jap. 41 (1995), 217--230). (English) |
| Keyword:
|
abstract integration |
| Keyword:
|
extension of integral |
| Keyword:
|
Kurzweil-Henstock integration |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| idZBL:
|
Zbl 1224.26031 |
| idMR:
|
MR2738961 |
| . |
| Date available:
|
2010-11-20T13:55:25Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140798 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/140797 |
| . |
| Reference:
|
[1] Bongiorno, B., Piazza, L. Di, Skvortsov, V.: A new full descriptive characterization of Denjoy-Perron integral.Real Anal. Exch. 21 (1995), 656-663. Zbl 0879.26026, MR 1407278, 10.2307/44152676 |
| Reference:
|
[2] Foran, J.: Fundamentals of Real Analysis.Marcel Dekker New York (1991). Zbl 0744.26004, MR 1201817 |
| Reference:
|
[3] Gordon, R. A.: The Integrals of Lebesgue, Denjoy, Perron and Henstock.American Mathematical Society Providence (1994). Zbl 0807.26004, MR 1288751 |
| Reference:
|
[4] Kubota, Y.: Abstract treatment of integration.Math. J. Ibaraki Univ. 29 (1997), 41-54. Zbl 0924.26005, MR 1601363, 10.5036/mjiu.29.41 |
| Reference:
|
[5] Kurzweil, J.: Nichtabsolut konvergente Integrale.BSB B. G. Teubner Verlagsgesellschaft Leipzig (1980). Zbl 0441.28001, MR 0597703 |
| Reference:
|
[6] Lee, P.-Y.: Lanzhou Lectures on Henstock Integration.World Scientific Singapore (1989). Zbl 0699.26004, MR 1050957 |
| Reference:
|
[7] Lee, P.-Y., Výborný, R.: The Integral; An Easy Approach after Kurzweil and Henstock.Cambridge Univ. Press Cambridge (2000). MR 1756319 |
| Reference:
|
[8] Nakanishi, S.: A new definition of the Denjoy's special integral by the method of successive approximation.Math. Jap. 41 (1995), 217-230. Zbl 0932.26007, MR 1317766 |
| Reference:
|
[9] Saks, S.: Theory of the Integral.Hafner New York (1937). Zbl 0017.30004 |
| Reference:
|
[10] Schwabik, Š.: Variational measures and the Kurzweil-Henstock integral.Math. Slovaca 59 (2009), 731-752. MR 2564330, 10.2478/s12175-009-0160-1 |
| Reference:
|
[11] Schwabik, Š.: General integration and extensions I.Czech. Math. J. 60 (2010), 961-981. MR 2738960, 10.1007/s10587-010-0087-2 |
| Reference:
|
[12] Thomson, B. S.: Derivates of Interval Functions.Mem. Am. Math. Soc. 452 (1991). Zbl 0734.26003, MR 1078198 |
| . |
