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

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1. Bochner S., 10.4064/fm-20-1-262-176, Fund. Math. 20 (1933) 262-276. (1933) Zbl0007.10901DOI10.4064/fm-20-1-262-176
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., 10.24033/asens.692, Ann. Еc. Norm. Sup. 33 (1916) 127-222. (1916) MR1509194DOI10.24033/asens.692
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

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