Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields

Jean Mawhin

Czechoslovak Mathematical Journal (1981)

  • Volume: 31, Issue: 4, page 614-632
  • ISSN: 0011-4642

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Mawhin, Jean. "Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields." Czechoslovak Mathematical Journal 31.4 (1981): 614-632. <http://eudml.org/doc/13290>.

@article{Mawhin1981,
author = {Mawhin, Jean},
journal = {Czechoslovak Mathematical Journal},
keywords = {Gauß’ theorem; differentiable vector fields; modification of Kurzweil-Henstock integral; Perron and Denjoy integral},
language = {eng},
number = {4},
pages = {614-632},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields},
url = {http://eudml.org/doc/13290},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Mawhin, Jean
TI - Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields
JO - Czechoslovak Mathematical Journal
PY - 1981
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 31
IS - 4
SP - 614
EP - 632
LA - eng
KW - Gauß’ theorem; differentiable vector fields; modification of Kurzweil-Henstock integral; Perron and Denjoy integral
UR - http://eudml.org/doc/13290
ER -

References

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  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. (1955) Zbl0068.28402MR0072224
  3. Bochner S., Green-Goursat theorem, Math. Z. 63 (1955) 230-242. (1955) Zbl0065.04102MR0072223
  4. Denjoy A., Memoire sur la totalisation des nombres dérivés non sommables, Ann. Еc. Norm. Sup. 33 (1916) 127-222. (1916) MR1509194
  5. Graves L. M., Riemann Integration and Taylor's theorem in general analysis, Trans. Amer. Math. Soc. 29 (1927) 163-177. (1927) MR1501382
  6. [61 Henstock R., Definitions of Riemann type of the variational integral, Proc. London Math. Soc. (3) 11 (1961) 402-418. (1961) MR0132147
  7. Henstock R., 10.4153/CJM-1968-010-5, Butterworths, London, 1963. (1963) Zbl0154.05001MR0158047DOI10.4153/CJM-1968-010-5
  8. Henstock R., A Riemann-type integral of Lebesgue power, Canadian J. Math. 20 (1968) 79-87. (1968) Zbl0171.01804MR0219675
  9. Henstock R., Linear Analysis, Butterworths, London, 1968. (1968) MR0419707
  10. Henstock R., Generalized integrals of vector-valued functions, Proc. London Math. Soc. (3) 19 (1969) 509-536. (1969) Zbl0176.33903MR0251189
  11. Henstock R., Additivity and the Lebesgue limit theorems, in "C. Caratheodory Symposium", Greek Math. Society, Athens, 1974, 223-241. (1974) Zbl0369.28003MR0466477
  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. (1957) Zbl0090.30002MR0111875
  13. Kurzweil J., On Fubini theorem for general Perron integral, Czechoslovak Math, J. 23 (98) (1973) 286-299. (1973) Zbl0267.26006MR0333086
  14. Kurzweil J., The Perron-Ward integral and related concepts, Appendix A in K. Jacobs, "Measure and Integral", Academic Press, New York, 1978. (1978) MR0514702
  15. Mawhin J., Introduction à l'Analyse, Cabay, Louvain-la-Neuve, 1979. (1979) Zbl0444.26002
  16. Mawhin J., Generalized Riemann integrals and the divergence theorem for differentiable vector fields, in Proceed. Intern. Christoffel Symposium, Birkhauser, Basel, 1980, to appear. (1980) MR0661109
  17. McShane E. J., A Riemann-type integral that includes Lebesgue-Stieltjes, Bochner and stochastic integrals, Mem. Amer. Math. Soc. 88 (1969) 1-54. (1969) Zbl0188.35702MR0265527
  18. Perron O., Über den Integralbegriff, S. В. Heidelberger Akad. Wiss. А 14 (1914), 1-16. (1914) 
  19. Schwartz L., 10.1112/jlms/s1-32.3.261, Hermann, Paris, 1967. (1967) DOI10.1112/jlms/s1-32.3.261
  20. Shapiro V. L., On Green's theorem, J. London Math. Soc. 32 (1957) 261-269. (1957) Zbl0079.27902MR0089275
  21. Spivak M., Calculus on Manifolds, Benjamin, New York, 1965. (1965) Zbl0141.05403MR0209411

Citations in EuDML Documents

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  1. Jiří Jarník, Jaroslav Kurzweil, Štefan Schwabik, On Mawhin's approach to multiple nonabsolutely convergent integral
  2. Josef Král, Note on generalized multiple Perron integral
  3. Shu Sheng Fu, A note on the GP-integral
  4. Jaroslav Kurzweil, Jiří Jarník, Equivalent definitions of regular generalized Perron integral
  5. Jiří Jarník, Jaroslav Kurzweil, A non-absolutely convergent integral which admits C 1 -transformations
  6. D. J. F. Nonnenmacher, Every M 1 -integrable function is Pfeffer integrable
  7. Jiří Jarník, Jaroslav Kurzweil, A non absolutely convergent integral which admits transformation and can be used for integration on manifolds
  8. Luisa Di Piazza, Variational measures in the theory of the integration in m
  9. Jiří Jarník, Jaroslav Kurzweil, Another Perron type integration in n dimensions as an extension of integration of stepfunctions
  10. Dirk Jens F. Nonnenmacher, A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

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