| Title:
|
Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields (English) |
| Author:
|
Mawhin, Jean |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
31 |
| Issue:
|
4 |
| Year:
|
1981 |
| Pages:
|
614-632 |
| Summary lang:
|
Russian |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A39 |
| MSC:
|
26A42 |
| MSC:
|
58C99 |
| idZBL:
|
Zbl 0562.26004 |
| idMR:
|
MR631606 |
| DOI:
|
10.21136/CMJ.1981.101777 |
| . |
| Date available:
|
2008-06-09T14:46:27Z |
| Last updated:
|
2020-07-28 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/101777 |
| . |
| Reference:
|
[1] Bochner S.: Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind.Fund. Math. 20 (1933) 262-276. Zbl 0007.10901, 10.4064/fm-20-1-262-176 |
| Reference:
|
[2] Bochner S.: Functions in one complex variable as viewed from the theory of functions in several variables.in "Lectures on Functions of a Complex Variable", W. Kaplan ed., Univ. Michigan Press, Ann. Arbor, 1955, 315-333. Zbl 0068.28402, MR 0072224 |
| Reference:
|
[3] Bochner S.: Green-Goursat theorem.Math. Z. 63 (1955) 230-242. Zbl 0065.04102, MR 0072223 |
| Reference:
|
[4] Denjoy A.: Memoire sur la totalisation des nombres dérivés non sommables.Ann. Еc. Norm. Sup. 33 (1916) 127-222. MR 1509194, 10.24033/asens.692 |
| Reference:
|
[5] Graves L. M.: Riemann Integration and Taylor's theorem in general analysis.Trans. Amer. Math. Soc. 29 (1927) 163-177. MR 1501382 |
| Reference:
|
[61 Henstock R.: Definitions of Riemann type of the variational integral.Proc. London Math. Soc. (3) 11 (1961) 402-418. MR 0132147 |
| Reference:
|
[7] Henstock R.: Theory of Integration.Butterworths, London, 1963. Zbl 0154.05001, MR 0158047, 10.4153/CJM-1968-010-5 |
| Reference:
|
[8] Henstock R.: A Riemann-type integral of Lebesgue power.Canadian J. Math. 20 (1968) 79-87. Zbl 0171.01804, MR 0219675 |
| Reference:
|
[9] Henstock R. : Linear Analysis.Butterworths, London, 1968. MR 0419707 |
| Reference:
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[10] Henstock R. : Generalized integrals of vector-valued functions.Proc. London Math. Soc. (3) 19 (1969) 509-536. Zbl 0176.33903, MR 0251189 |
| Reference:
|
[11] Henstock R.: Additivity and the Lebesgue limit theorems.in "C. Caratheodory Symposium", Greek Math. Society, Athens, 1974, 223-241. Zbl 0369.28003, MR 0466477 |
| Reference:
|
[12] Kurzweil J.: Generalized ordinary differential equations and continuous dependence on a parameter.Czechoslovak Math. J. 7 (82) (1957) 418-446. Addition, ibid 9 (84) (1959), 564-573. Zbl 0090.30002, MR 0111875 |
| Reference:
|
[13] Kurzweil J.: On Fubini theorem for general Perron integral.Czechoslovak Math, J. 23 (98) (1973) 286-299. Zbl 0267.26006, MR 0333086 |
| Reference:
|
[14] Kurzweil J.: The Perron-Ward integral and related concepts.Appendix A in K. Jacobs, "Measure and Integral", Academic Press, New York, 1978. MR 0514702 |
| Reference:
|
[15] Mawhin J.: Introduction à l'Analyse.Cabay, Louvain-la-Neuve, 1979. Zbl 0444.26002 |
| Reference:
|
[16] Mawhin J.: Generalized Riemann integrals and the divergence theorem for differentiable vector fields.in Proceed. Intern. Christoffel Symposium, Birkhauser, Basel, 1980, to appear. MR 0661109 |
| Reference:
|
[17] McShane E. J.: A Riemann-type integral that includes Lebesgue-Stieltjes.Bochner and stochastic integrals, Mem. Amer. Math. Soc. 88 (1969) 1-54. Zbl 0188.35702, MR 0265527 |
| Reference:
|
[18] Perron O.: Über den Integralbegriff.S. В. Heidelberger Akad. Wiss. А 14 (1914), 1-16. |
| Reference:
|
[19] Schwartz L.: Cours d'analyse.Hermann, Paris, 1967. 10.1112/jlms/s1-32.3.261 |
| Reference:
|
[20] Shapiro V. L.: On Green's theorem.J. London Math. Soc. 32 (1957) 261-269. Zbl 0079.27902, MR 0089275 |
| Reference:
|
[21] Spivak M.: Calculus on Manifolds.Benjamin, New York, 1965. Zbl 0141.05403, MR 0209411 |
| . |
