Geodesic
Nonstandard analysis and generalized Riemann integrals
Časopis pro pěstování matematiky, Tome 111 (1986) no. 1, pp. 34-47

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

DOI MR   Zbl

DOI : 10.21136/CPM.1986.118262
Classification : 26A42 
Mawhin, Jean. Nonstandard analysis and generalized Riemann integrals. Časopis pro pěstování matematiky, Tome 111 (1986) no. 1, pp. 34-47. doi: 10.21136/CPM.1986.118262
@article{10_21136_CPM_1986_118262,
     author = {Mawhin, Jean},
     title = {Nonstandard analysis and generalized {Riemann} integrals},
     journal = {\v{C}asopis pro p\v{e}stov\'an{\'\i} matematiky},
     pages = {34--47},
     year = {1986},
     volume = {111},
     number = {1},
     doi = {10.21136/CPM.1986.118262},
     mrnumber = {833155},
     zbl = {0601.26005},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.21136/CPM.1986.118262/}
}
TY  - JOUR
AU  - Mawhin, Jean
TI  - Nonstandard analysis and generalized Riemann integrals
JO  - Časopis pro pěstování matematiky
PY  - 1986
SP  - 34
EP  - 47
VL  - 111
IS  - 1
UR  - http://geodesic.mathdoc.fr/articles/10.21136/CPM.1986.118262/
DO  - 10.21136/CPM.1986.118262
LA  - en
ID  - 10_21136_CPM_1986_118262
ER  - 
%0 Journal Article
%A Mawhin, Jean
%T Nonstandard analysis and generalized Riemann integrals
%J Časopis pro pěstování matematiky
%D 1986
%P 34-47
%V 111
%N 1
%U http://geodesic.mathdoc.fr/articles/10.21136/CPM.1986.118262/
%R 10.21136/CPM.1986.118262
%G en
%F 10_21136_CPM_1986_118262

[1] P. J. Cohen: Set Theory and the Continuum hypothesis. Benjamin, New York, 1966. | MR | Zbl

[2] N. J. Cutland: Nonstandard measure theory and its applications. Bull. London Math. Soc. 75 (1983), 529-589. | MR | Zbl

[3] F. Diener: Cours d'analyse non-standard. Oran, 1983.

[4] R. Henstock: Definitions of the Riemann type of the variational integrals. Proc. London Math. Soc. (3) II (1961), 402-418. | MR

[5] R. Henstock: Theory of Integration. Butter worths, London, 1963. | MR | Zbl

[6] R. Henstock: Linear Analysis. Butterworth, London, 1967. | MR | Zbl

[7] J. Jarník, J. Kurzweil: A non-absolutely convergent integral which admits C1-transformations. Časopis pěst. mat. 109 (1984), 157-167. | MR

[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 (710) (1985), 116-139. | MR

[9] J. Jarník J. Kurzweil, S. Schwabik: On Mawhin's approach to multiple nonabsolutely convergent integrals. Časopis pěst. mat. 108 (1983), 356-380. | MR

[10] J. Kurzweil: Generalized ordinary differential equations and continuous dependence on a parameter. Czechoslovak Math. J. 7 (82) (1957), 418-446. | MR | Zbl

[11] J. Kurzweil: Nichtabsolut konvergente Integrale. Teubner, Leipzig, 1980. | MR | Zbl

[12] J. Kurzweil: The integral as a limit of integral sums. in: Jahrbuch Oberblicke Mathematik. Bibliographisches Institut, 1984, 105-136. | Zbl

[13] P. A. Loeb: Conversion from nonstandard to standard measure spaces and applications in probability theory. Trans. Amer. Math. Soc. 277 (1975), 113-122. | MR | Zbl

[14] R. Lutz, M. Goze: Nonstandard Analysis. Lect. Notes in Math. No 881, Springer, Berlin, 1981. | MR | Zbl

[15] J. Mawhin: Introduction à l'Analyse. 4e edition, Cabay, Louvain-la-Neuve, 1984.

[16] J. Mawhin: Generalized Riemann integrals and the divergence theorem for differentiable vector fields. in: E. B. Christoffel, Butzer ed., Birkhauser, Bassel, 1981, 704-714. | MR | Zbl

[17] J. Mawhin: Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields. Czechoslovak Math. J. 37 (706) (1981), 614-632. | MR | Zbl

[18] R. M. McLeod: The Generalized Riemann Integral. Carus Math. Monographs No 20, Math. Assoc. America, Washington, 1980. | MR | Zbl

[19] E. J. McShane: Unified Integration. Academic Press, Orlando, 1983. | MR | Zbl

[20] E. Nelson: Internal set theory: a new approach to nonstandard analysis. Bull. Amer. Math. Soc. 83 (1977), 1165-1198. | MR | Zbl

[21] O. Perron: Über den Integralbegriff. Sitzber. Heidelberg Akad. Wiss. A16 (1914) 1-16.

[22] W. F. Pfeffer: The Riemann-Stieltjes approach to integration. Twisk 187, N.R.I.M.S., C.S.I.R., Pretoria, 1980.

[23] W. F. Pfeffer: Une integrale riemanienne et le theorems de divergence. C. R. Acad. Sci. Paris 299, Ser. I, (1984), 299-301. | MR

[24] W. F. Pfeffer: The divergence theorem. Univ. Petroleum and Minerals Dhraran, Saudi Arabia, Techn. Rept. No 64, 1984. | Zbl

[25] A. Robinson: Nonstandard analysis. Proc. Roy. Аcad. Sci. Аmsterdam А 64 (1961), 432-440. | MR

[26] A. Robinson: Introduction to Model Theory and to the Metamathematics of Аlgebra. North-Holland, Аmsterdam, 1965. | MR

[27] A. Robinson: Nonstandard Аnalysis. North-Holland, Аmsterdam, 1967

[28] B. S. Thomson: Derivation bases on the real line. Real Аnal. Exchange 8 (1982-83), 67-207, 278-442.

Cité par Sources :