| Title:
|
Gauge integrals and series (English) |
| Author:
|
Swartz, Charles |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
129 |
| Issue:
|
3 |
| Year:
|
2004 |
| Pages:
|
325-332 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
This note contains a simple example which does clearly indicate the differences in the Henstock-Kurzweil, McShane and strong McShane integrals for Banach space valued functions. (English) |
| Keyword:
|
Henstock-Kurzweil integral |
| Keyword:
|
McShane integral |
| MSC:
|
26A39 |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1080.28008 |
| idMR:
|
MR2092718 |
| DOI:
|
10.21136/MB.2004.134147 |
| . |
| Date available:
|
2009-09-24T22:15:42Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134147 |
| . |
| Reference:
|
[1] M. Day: Normed Linear Spaces.Springer, New York, 1962. Zbl 0100.10802 |
| Reference:
|
[2] D. H. Fremlin: The Henstock and McShane integrals of vector-valued functions.Illinois J. Math. 38 (1994), 471–479. Zbl 0797.28006, MR 1269699, 10.1215/ijm/1255986726 |
| Reference:
|
[3] D. H. Fremlin, J. Mendoza: On the integration of vector-valued functions.Illinois J. Math. 38 (1994), 127–147. MR 1245838, 10.1215/ijm/1255986891 |
| Reference:
|
[4] R. Gordon: The Integrals of Lebesgue, Denjoy, Perron and Henstock.Amer. Math. Soc., Providence, 1991. MR 1288751 |
| Reference:
|
[5] R. Gordon: The McShane integral of Banach-valued functions.Illinois J. Math. 34 (1990), 557–567. Zbl 0685.28003, MR 1053562, 10.1215/ijm/1255988170 |
| Reference:
|
[6] E. Hille, R. Phillips: Functional Analysis and Semigroups.Amer. Math. Soc., Providence, 1957. MR 0089373 |
| Reference:
|
[7] Peng Yee Lee, R. Výborný: The Integral: an Easy Approach after Kurzweil and Henstock.Cambridge Univ. Press, Cambridge, 2000. MR 1756319 |
| Reference:
|
[8] E. J. McShane: Unified Integration.Academic Press, New York, 1983. Zbl 0551.28001, MR 0740710 |
| Reference:
|
[9] W. Pfeffer: The Riemann Approach to Integration.Cambridge Univ. Press, Cambridge, 1993. Zbl 0804.26005, MR 1268404 |
| Reference:
|
[10] Š. Schwabik: Abstract Bochner and McShane integrals.Ann. Math. Silesianae 10 (1996), 21–56. Zbl 0868.28005, MR 1399609 |
| Reference:
|
[11] Š. Schwabik, Guoju Ye: 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: Beppo Levi’s theorem for the vector-valued McShane integral and applications.Bull. Belgian Math. Soc. 4 (1997), 589–599. Zbl 1038.46505, MR 1600292, 10.36045/bbms/1105737762 |
| Reference:
|
[13] C. Swartz: Infinite Matrices and the Gliding Hump.World Sci. Publ., Singapore, 1996. Zbl 0923.46003, MR 1423136 |
| Reference:
|
[14] C. Swartz: Introduction to Gauge Integrals.World Scientific Publ., Singapore, 2001. Zbl 0982.26006, MR 1845270 |
| Reference:
|
[15] Wu Congin, Yao Xiaobo: A Riemann-type definition of the Bochner integral.J. Math. Study 27 (1994), 32–36. MR 1318255 |
| . |
