| Title:
|
Riemann-type definition of the improper integrals (English) |
| Author:
|
Bongiorno, Donatella |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
54 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
717-725 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Riemann-type definitions of the Riemann improper integral and of the Lebesgue improper integral are obtained from McShane’s definition of the Lebesgue integral by imposing a Kurzweil-Henstock’s condition on McShane’s partitions. (English) |
| Keyword:
|
McShane’s partition |
| Keyword:
|
Kurzweil-Henstock’s partition |
| MSC:
|
26A36 |
| MSC:
|
26A39 |
| idZBL:
|
Zbl 1080.26003 |
| idMR:
|
MR2086728 |
| . |
| Date available:
|
2009-09-24T11:16:50Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127923 |
| . |
| Reference:
|
[1] B. Bongiorno: Un nuovo integrale per il problema delle primitive.Le Matematiche 51 (1996), 299–313. |
| Reference:
|
[2] B. Bongiorno, L. Di Piazza and D. Preiss: A constructive minimal integral which includes Lebesgue integrable functions and derivatives.J. London Math. Soc. 62 (2000), 117–126. MR 1771855, 10.1112/S0024610700008905 |
| Reference:
|
[3] A. M. Bruckner, R. J. Fleissner and J. Foran: The minimal integral which includes Lebesgue integrable functions and derivatives.Coll. Math. 50 (1986), 289–293. MR 0857865, 10.4064/cm-50-2-289-293 |
| Reference:
|
[4] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Lebesgue. Graduate Studies in Math.vol. 4, AMS, 1994. MR 1288751 |
| Reference:
|
[5] E. J. McShane: A unified theory of integration.Amer. Math. Monthly 80 (1973), 349–359. Zbl 0266.26008, MR 0318434, 10.2307/2319078 |
| Reference:
|
[6] K. Kurzweil: Nichtabsolut Konvergente Integrale.Teubner, Leipzig, 1980. Zbl 0441.28001, MR 0597703 |
| Reference:
|
[7] W. F. Pfeffer: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 0804.26005, MR 1268404 |
| Reference:
|
[8] S. Saks: Theory of the Integral.Dover, New York, 1964. MR 0167578 |
| . |
