| Title:
|
A Daniell integral approach to nonstandard Kurzweil-Henstock integral (English) |
| Author:
|
Bianconi, Ricardo |
| Author:
|
Prandini, João C. |
| Author:
|
Possani, Cláudio |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
49 |
| Issue:
|
4 |
| Year:
|
1999 |
| Pages:
|
817-823 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A workable nonstandard definition of the Kurzweil-Henstock integral is given via a Daniell integral approach. This allows us to study the HL class of functions from . The theory is recovered together with a few new results. (English) |
| MSC:
|
03H05 |
| MSC:
|
26A39 |
| MSC:
|
26E35 |
| MSC:
|
28A25 |
| MSC:
|
28E05 |
| idZBL:
|
Zbl 1008.26021 |
| idMR:
|
MR1746706 |
| . |
| Date available:
|
2009-09-24T10:27:53Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127530 |
| . |
| Reference:
|
[albev] S. Albeverio, J. E. Fenstad, R. Høegh-Krohn, and T. Lindstrøm: Nonstandard methods in stochastic analysis and mathematical physics.Academic Press, Orlando, 1986. MR 0859372 |
| Reference:
|
[ben] B. Benninghofen: Superinfinitesimals and the calculus of the generalized Riemann integral.Models and sets (Aachen, 1983), Lect. Notes in Math., 1103, Springer, Berlin-New York, pp. 9–52. Zbl 0583.26005, MR 0775686 |
| Reference:
|
[bi] R. Bianconi: A note on frameworks of nonstandard analysis, in preparation.. |
| Reference:
|
[bipra] R. Bianconi, J. C. Prandini: Nonstandard Henstock-Kurzweil integralProc. 42nd. SBA.(1995, 669–681). |
| Reference:
|
[revHe] R. Henstock: Review of.Mathematical Reviews, 86g:26008. |
| Reference:
|
[he] R. Henstock: Lectures on the theory of integration.Series in Real Analysis Volume 1, World Scientific, Singapore, 1988. Zbl 0668.28001, MR 0963249 |
| Reference:
|
[hurdloeb] A. E. Hurd, P. A. Loeb: An introduction to nonstandard real analysis.Academic Press, Orlando, 1985. MR 0806135 |
| Reference:
|
[keisler] H. J. Keisler: Elementary calculus.Prindle, Weber and Schmidt, Boston, 1976. Zbl 0325.26001 |
| Reference:
|
[lanzhou] Lee Peng-Yee: Lanzhou lectures on Henstock integration.Series in Real Analysis Volume 2, World Scientific, Singapore, 1989. Zbl 0699.26004, MR 1050957 |
| Reference:
|
[schwabik] S. Schwabik: Generalized ordinary differential equations.Series in Real Analysis Volume 5, World Scientific, Singapore, 1992. Zbl 0781.34003, MR 1200241 |
| . |
