| Title:
|
Riemann type integrals for functions taking values in a locally convex space (English) |
| Author:
|
Marraffa, V. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
56 |
| Issue:
|
2 |
| Year:
|
2006 |
| Pages:
|
475-490 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
The McShane and Kurzweil-Henstock integrals for functions taking values in a locally convex space are defined and the relations with other integrals are studied. A characterization of locally convex spaces in which Henstock Lemma holds is given. (English) |
| Keyword:
|
Pettis integral |
| Keyword:
|
McShane integral |
| Keyword:
|
Kurzweil-Henstock integral |
| Keyword:
|
locally convex spaces |
| MSC:
|
26A42 |
| MSC:
|
26E20 |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1164.28304 |
| idMR:
|
MR2291749 |
| . |
| Date available:
|
2009-09-24T11:34:39Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128079 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
[3] L. Di Piazza, K. Musiał: A characterization of variationally McShane integrable Banach-space valued functions.Illinois J. Math. 45 (2001), 279–289. MR 1849999, 10.1215/ijm/1258138268 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[6] 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:
|
[7] R. A. 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:
|
[8] V. Marraffa: The McShane integral in a locally convex space.Rocky Mountain J. (2006) (to appear). |
| Reference:
|
[9] C. W. McArthur, J. R. Retherford: Some applications of an inequality in locally convex spaces.Trans. Amer. Math. Soc. 137 (1969), 115–123. MR 0239391, 10.1090/S0002-9947-1969-0239391-0 |
| Reference:
|
[10] S. Nakanishi: The Henstock integral for functions with values in nuclear spaces.Math. Japonica 39 (1994), 309–335. Zbl 0927.26011, MR 1270642 |
| Reference:
|
[11] K. Sakurada, S. Nakanishi: Equivalence of the McShane and Bochner integrals for functions with values in Hilbertian (UCs-N) spaces endowed with nuclearity.Math. Japonica 47 (1998), 261–272. MR 1615121 |
| Reference:
|
[12] A. Pietsch: Nuclear Locally Convex Spaces.Springer-Verlag, Berlin and New York, 1972. Zbl 0308.47024, MR 0350360 |
| Reference:
|
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| Reference:
|
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| . |
