| Title:
|
A scalar Volterra derivative for the PoU-integral (English) |
| Author:
|
Marraffa, V. |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
130 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
49-62 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
A weak form of the Henstock Lemma for the ${\mathrm PoU}$-integrable functions is given. This allows to prove the existence of a scalar Volterra derivative for the ${\mathrm PoU}$-integral. Also the ${\mathrm PoU}$-integrable functions are characterized by means of Pettis integrability and a condition involving finite pseudopartitions. (English) |
| Keyword:
|
Pettis integral |
| Keyword:
|
McShane integral |
| Keyword:
|
${\mathrm PoU}$ integral |
| Keyword:
|
Volterra derivative |
| MSC:
|
28B05 |
| MSC:
|
46G10 |
| idZBL:
|
Zbl 1112.28009 |
| idMR:
|
MR2128358 |
| DOI:
|
10.21136/MB.2005.134220 |
| . |
| Date available:
|
2009-09-24T22:17:55Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134220 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
|
[4] L. Di Piazza, V. Marraffa: An equivalent definition of the vector-valued McShane integral by means of partitions of the unity.Studia Math. 151 (2002), 175–185. MR 1917952, 10.4064/sm151-2-5 |
| Reference:
|
[5] N. Dunford, B. J. Pettis: Linear operations on summable functions.Trans. Amer. Math. Soc. 47 (1940), 323–392. MR 0002020, 10.1090/S0002-9947-1940-0002020-4 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[8] J. Jarník, J. Kurzweil: A non absolutely convergent integral which admits transformation and can be used for integration on manifolds.Czechoslovak Math. J. 35 (1985), 116–139. MR 0779340 |
| Reference:
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[9] J. Jarník, J. Kurzweil: A new and more powerful concept of the ${\mathrm PU}$-integral.Czechoslovak Math. J. 38 (1988), 8–48. MR 0925939 |
| Reference:
|
[10] B. J. Pettis: Differentiation in Banach space.Duke Math. J. 5 (1939), 254–269. MR 1546122, 10.1215/S0012-7094-39-00523-5 |
| Reference:
|
[11] W. F. Pfeffer: A Volterra type derivative of the Lebesgue integral.Proc. Amer. Math. Soc. 117 (1993), 411–416. Zbl 0789.28005, MR 1135079, 10.1090/S0002-9939-1993-1135079-1 |
| Reference:
|
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| Reference:
|
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| . |
