| Title:
|
The Kurzweil integral with exclusion of negligible sets (English) |
| Author:
|
Krejčí, Pavel |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
128 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
277-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We propose an extended version of the Kurzweil integral which contains both the Young and the Kurzweil integral as special cases. The construction is based on a reduction of the class of $\delta $-fine partitions by excluding small sets. (English) |
| Keyword:
|
Kurzweil integral |
| Keyword:
|
Young integral |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| idZBL:
|
Zbl 1051.26006 |
| idMR:
|
MR2012605 |
| DOI:
|
10.21136/MB.2003.134183 |
| . |
| Date available:
|
2009-09-24T22:09:48Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134183 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] T. H. Hildebrandt: Introduction to the Theory of Integration.Academic Press, New York and London, 1963. Zbl 0112.28302, MR 0154957 |
| Reference:
|
[4] P. Krejčí, J. Kurzweil: A nonexistence result for the Kurzweil integral.Math. Bohem. 127 (2002), 571–580. MR 1942642 |
| Reference:
|
[5] P. Krejčí, Ph. Laurençot: Generalized variational inequalities.J. Convex Anal. 9 (2002), 159–183. MR 1917394 |
| Reference:
|
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| Reference:
|
[7] Š. Schwabik: On the relation between Young’s and Kurzweil’s concept of Stieltjes integral.Čas. Pěst. Mat. 98 (1973), 237–251. Zbl 0266.26006, MR 0322113 |
| Reference:
|
[8] Š. Schwabik: On a modified sum integral of Stieltjes type.Čas. Pěst. Mat. 98 (1973), 274–277. Zbl 0266.26007, MR 0322114 |
| Reference:
|
[9] Š. Schwabik: Abstract Perron-Stieltjes integral.Math. Bohem. 121 (1996), 425–447. Zbl 0879.28021, MR 1428144 |
| Reference:
|
[10] M. Tvrdý: Regulated functions and the Perron-Stieltjes integral.Čas. Pěst. Mat. 114 (1989), 187–209. MR 1063765 |
| . |
