| Title:
|
A measure-theoretic characterization of the Henstock-Kurzweil integral revisited (English) |
| Author:
|
Lee, Tuo-Yeong |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
58 |
| Issue:
|
4 |
| Year:
|
2008 |
| Pages:
|
1221-1231 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we show that the measure generated by the indefinite Henstock-Kurzweil integral is $F_{\sigma \delta }$ regular. As a result, we give a shorter proof of the measure-theoretic characterization of the Henstock-Kurzweil integral. (English) |
| Keyword:
|
Henstock variational measure |
| Keyword:
|
Henstock-Kurzweil integral |
| MSC:
|
26A39 |
| idZBL:
|
Zbl 1174.26005 |
| idMR:
|
MR2471178 |
| . |
| Date available:
|
2010-07-21T08:16:30Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140452 |
| . |
| Reference:
|
[1] Bongiorno, D., Piazza, L. Di, Skvortsov, V. A.: Variational measures related to local systems and the ward property of ${\cal P}$-adic path bases.Czech. Math. J. 56 (2006), 559-578. Zbl 1164.26316, MR 2291756, 10.1007/s10587-006-0037-1 |
| Reference:
|
[2] Piazza, L. Di: Variational measures in the theory of the integration in ${\mathbb R}^m$.Czech. Math. J. 51 (2001), 95-110. MR 1814635, 10.1023/A:1013705821657 |
| Reference:
|
[3] Faure, Claude-Alain: A descriptive definition of some multidimensional gauge integrals.Czech. Math. J. 45 (1995), 549-562. Zbl 0852.26010, MR 1344520 |
| Reference:
|
[4] Henstock, R., Muldowney, P., Skvortsov, V. A.: Partitioning infinite-dimensional spaces for generalized Riemann integration.Bull. London Math. Soc. 38 (2006), 795-803. Zbl 1117.28010, MR 2268364, 10.1112/S0024609306018819 |
| Reference:
|
[5] Kurzweil, J., Jarník, J.: Differentiability and integrability in $n$ dimensions with respect to $\alpha$-regular intervals.Results Math. 21 (1992), 138-151. MR 1146639, 10.1007/BF03323075 |
| Reference:
|
[6] Tuo-Yeong, Lee: A full descriptive definition of the Henstock-Kurzweil integral in the Euclidean space.Proc. London Math. Soc. 87 (2003), 677-700. MR 2005879 |
| Reference:
|
[7] Tuo-Yeong, Lee: Product variational measures and Fubini-Tonelli type theorems for the Henstock-Kurzweil integral.J. Math. Anal. Appl. 298 (2004), 677-692. MR 2086983, 10.1016/j.jmaa.2004.05.033 |
| Reference:
|
[8] Tuo-Yeong, Lee: A characterisation of multipliers for the Henstock-Kurzweil integral.Math. Proc. Cambridge Philos. Soc. 138 (2005), 487-492. MR 2138575, 10.1017/S030500410500839X |
| Reference:
|
[9] Tuo-Yeong, Lee: The Henstock variational measure, Baire functions and a problem of Henstock.Rocky Mountain J. Math 35 (2005), 1981-1997. MR 2210644, 10.1216/rmjm/1181069626 |
| Reference:
|
[10] Tuo-Yeong, Lee: Some full descriptive characterizations of the Henstock-Kurzweil integral in the Euclidean space.Czech. Math. J. 55 (2005), 625-637. MR 2153087, 10.1007/s10587-005-0050-9 |
| Reference:
|
[11] Tuo-Yeong, Lee: Product variational measures and Fubini-Tonelli type theorems for the Henstock-Kurzweil integral II.J. Math. Anal. Appl. 323 (2006), 741-745. MR 2262241, 10.1016/j.jmaa.2005.10.045 |
| Reference:
|
[12] Thomson, B. S.: Derivates of interval functions.Mem. Amer. Math. Soc. 93 (1991). Zbl 0734.26003, MR 1078198 |
| Reference:
|
[13] Ward, A. J.: On the derivation of additive interval functions of intervals in $m$-dimensional space.Fund. Math. 28 (1937), 265-279. |
| . |
