| Title:
|
Some full characterizations of the strong McShane integral (English) |
| Author:
|
Lee, Tuo-Yeong |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
305-312 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Some full characterizations of the strong McShane integral are obtained. (English) |
| Keyword:
|
strong McShane integral |
| Keyword:
|
strong absolute continuity |
| Keyword:
|
McShane variational measure |
| MSC:
|
26A36 |
| MSC:
|
26A39 |
| MSC:
|
26B30 |
| idZBL:
|
Zbl 1080.26006 |
| idMR:
|
MR2092716 |
| DOI:
|
10.21136/MB.2004.134144 |
| . |
| Date available:
|
2009-09-24T22:15:28Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134144 |
| . |
| Reference:
|
[1] A. M. Bruckner, J. B. Bruckner, B. S. Thomson: Real Analysis.Prentice-Hall, 1997. |
| Reference:
|
[2] J. A. Clarkson: Uniformly convex spaces.Trans. Amer. Math. Soc. 40 (1936), 396–414. Zbl 0015.35604, MR 1501880, 10.1090/S0002-9947-1936-1501880-4 |
| Reference:
|
[3] L. Di Piazza: Variational measures in the theory of the integration in ${\mathbb{R}}^m$.Czechoslovak Math. J. 51 (2001), 95–110. MR 1814635, 10.1023/A:1013705821657 |
| Reference:
|
[4] D. H. Fremlin, J. Mendoza: On the integration of vector-valued functions.Illinois J. Math. 38 (1994), 127–141. MR 1245838, 10.1215/ijm/1255986891 |
| Reference:
|
[5] R. A. Gordon: The Integrals of Lebesgue, Denjoy, Perron, and Henstock.Amer. Math. Soc., Providence, 1994. Zbl 0807.26004, MR 1288751 |
| Reference:
|
[6] J. Jarník, J. Kurzweil: Perron-type integration on $n$-dimensional intervals and its properties.Czechoslovak Math. J. 45 (1995), 79–106. MR 1314532 |
| Reference:
|
[7] Lee Peng Yee, R. Výborný: The Integral, An Easy Approach after Kurzweil and Henstock.Australian Mathematical Society Lecture Ser. 14, Cambridge University Press, 2000. MR 1756319 |
| Reference:
|
[8] Lee Tuo-Yeong: Every absolutely Henstock-Kurzweil integrable function is McShane integrable: an alternative proof.(to appear). Zbl 1064.28011, MR 2095582 |
| Reference:
|
[9] W. F. Pfeffer: A note on the generalized Riemann integral.Proc. Amer. Math. Soc. 103 (1988), 1161–1166. Zbl 0656.26010, MR 0955000, 10.1090/S0002-9939-1988-0955000-4 |
| Reference:
|
[10] W. F. Pfeffer: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 0804.26005, MR 1268404 |
| Reference:
|
[11] Š. Schwabik, Ye Guoju: On the strong McShane integral of functions with values in a Banach space.Czechoslovak Math. J. 51 (2001), 819–828. MR 1864044, 10.1023/A:1013721114330 |
| Reference:
|
[12] C. Swartz: Introduction to the Gauge Integrals.World Scientific, 2001. MR 1845270 |
| Reference:
|
[13] B. S. Thomson: Derivates of Interval Functions.Mem. Amer. Math. Soc. 452, 1991. Zbl 0734.26003, MR 1078198 |
| . |
