| Title:
|
A step to Kurzweil-Henstock—an outline (English) |
| Author:
|
Craven, B. D. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
297-304 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A short approach to the Kurzweil-Henstock integral is outlined, based on approximating a real function on a compact interval by suitable step-functions, and using filterbase convergence to define the integral. The properties of the integral are then easy to establish. (English) |
| Keyword:
|
integral |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
step-function |
| Keyword:
|
filterbase |
| MSC:
|
26A39 |
| idZBL:
|
Zbl 1080.26004 |
| idMR:
|
MR2092715 |
| DOI:
|
10.21136/MB.2004.134150 |
| . |
| Date available:
|
2009-09-24T22:15:19Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134150 |
| . |
| Reference:
|
[1] B. D. Craven: Lebesgue Measure and Integral.Pitman, Boston, 1982. Zbl 0491.28001, MR 0733102 |
| Reference:
|
[2] J. Dugundji: Topology.Allyn & Bacon, Boston, 1966. Zbl 0144.21501, MR 0193606 |
| Reference:
|
[3] R. Henstock: Linear Analysis.Butterworths, 1967. Zbl 0172.39001, MR 0419707 |
| Reference:
|
[4] R. Henstock: The General Theory of Integration.Clarendon Press, Oxford, U.K., 1991. Zbl 0745.26006, MR 1134656 |
| Reference:
|
[5] J. Kurzweil: Nichtabsolut konvergente Intgegrale.Teubner, Leipzig, 1980. MR 0597703 |
| Reference:
|
[6] S. Leader: The Kurzweil-Henstock Integral and its Differentials.Marcel Dekker, New York, 2001. Zbl 0984.26002, MR 1837270 |
| Reference:
|
[7] Lee Peng-Yee: Lanzhou Lectures on Integration.World Scientific, Singapore, 1989. MR 1050957 |
| Reference:
|
[8] Lee Peng-Yee, R. Výborný: The Integral: an easy approach after Kurzweil and Henstock.Cambridge University Press, 2000. MR 1756319 |
| Reference:
|
[9] E. Schechter: Handbook of Analysis and its Foundations.Academic Press, San Diego, 1997 (Chapter 24: Generalized Riemann integrals). MR 1417259 |
| Reference:
|
[10] Š. Schwabik: Integration on $\mathbb{R}$: Kurzweil Theory.Charles University, Praha, 1999. (Czech) |
| . |
