| Title:
|
A nonexistence result for the Kurzweil integral (English) |
| Author:
|
Krejčí, Pavel |
| Author:
|
Kurzweil, Jaroslav |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
127 |
| Issue:
|
4 |
| Year:
|
2002 |
| Pages:
|
571-580 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
It is shown that there exist a continuous function $f$ and a regulated function $g$ defined on the interval $[0,1]$ such that $g$ vanishes everywhere except for a countable set, and the $K^*$-integral of $f$ with respect to $g$ does not exist. The problem was motivated by extensions of evolution variational inequalities to the space of regulated functions. (English) |
| Keyword:
|
Kurzweil integral |
| Keyword:
|
regulated functions |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| idZBL:
|
Zbl 1005.26005 |
| idMR:
|
MR1942642 |
| DOI:
|
10.21136/MB.2002.133949 |
| . |
| Date available:
|
2009-09-24T22:05:15Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/133949 |
| . |
| Reference:
|
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| Reference:
|
[2] D. Fraňková: Regulated functions.Math. Bohem. 119 (1991), 20–59. MR 1100424 |
| Reference:
|
[3] T. H. Hildebrandt: Introduction to the theory of integration.Academic Press, New York, 1963. Zbl 0112.28302, MR 0154957 |
| Reference:
|
[4] P. Krejčí, Ph. Laurençot: Generalized variational inequalities.J. Convex Anal. 9 (2002), 159–183. MR 1917394 |
| Reference:
|
[5] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslovak Math. J. 7 (1957), 418–449. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[6] Š. Schwabik: On the relation between Young’s and Kurzweil’s concept of Stieltjes integral.Časopis Pěst. Mat. 98 (1973), 237–251. Zbl 0266.26006, MR 0322113 |
| Reference:
|
[7] Š. Schwabik: On a modified sum integral of Stieltjes type.Časopis Pěst. Mat. 98 (1973), 274–277. Zbl 0266.26007, MR 0322114 |
| Reference:
|
[8] Š. Schwabik, M. Tvrdý, O. Vejvoda: Differential and Integral Equations: Boundary Value Problems and Adjoints.Academia and D. Reidel, Praha, 1979. MR 0542283 |
| Reference:
|
[9] M. Tvrdý: Regulated functions and the Perron-Stieltjes integral.Časopis Pěst. Mat. 114 (1989), 187–209. MR 1063765 |
| . |
