| Title:
|
Denjoy integral and Henstock-Kurzweil integral in vector lattices. I (English) |
| Author:
|
Kawasaki, Toshiharu |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
59 |
| Issue:
|
2 |
| Year:
|
2009 |
| Pages:
|
381-399 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper we define the derivative and the Denjoy integral of mappings from a vector lattice to a complete vector lattice and show the fundamental theorem of calculus. (English) |
| Keyword:
|
derivative |
| Keyword:
|
Denjoy integral |
| Keyword:
|
Henstock-Kurzweil integral |
| Keyword:
|
fundamental theorem of calculus |
| Keyword:
|
vector lattice |
| Keyword:
|
Riesz space |
| MSC:
|
26A39 |
| MSC:
|
46B42 |
| MSC:
|
46G05 |
| MSC:
|
46G10 |
| MSC:
|
46G12 |
| idZBL:
|
Zbl 1224.46083 |
| idMR:
|
MR2532373 |
| . |
| Date available:
|
2010-07-20T15:15:05Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/140487 |
| . |
| Related article:
|
http://dml.cz/handle/10338.dmlcz/140488 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
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[3] Cristescu, R.: Ordered Vector Spaces and Linear Operators.Abacus Press (1976). Zbl 0322.46010, MR 0467238 |
| Reference:
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[4] Izumi, S.: An abstract integral (X).Proc. Imp. Acad. Japan 18 (1942), 543-547. Zbl 0061.09909, MR 0021080, 10.3792/pia/1195573784 |
| Reference:
|
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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[10] Kawasaki, T.: Order derivative and order Newton integral of operators in vector lattices.Far East J. Math. Sci. 1 (1999), 903-926. Zbl 1069.46507, MR 1734826 |
| Reference:
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[11] Kawasaki, T.: Uniquely determinedness of the approximately order derivative.Sci. Math. Japonicae Online 7 (2002), 333-336 Sci. Math. Japonicae 57 (2003), 365-371. Zbl 1039.46036, MR 1959995 |
| Reference:
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[12] Kubota, Y.: Theory of the Integral.Japanese Maki (1977). |
| Reference:
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[13] Lee, P. Y.: Lanzhou Lectures on Henstock Integration.World Scientific (1989). Zbl 0699.26004, MR 1050957 |
| Reference:
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[14] Luxemburg, W. A. J., Zaanen, A. C.: Riesz Spaces.North-Holland (1971). Zbl 0231.46014 |
| Reference:
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| Reference:
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| Reference:
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| Reference:
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| Reference:
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