@article{10_21136_CMJ_1995_128532,
author = {Faure, Claude-Alain},
title = {A descriptive definition of some multidimensional gauge integrals},
journal = {Czechoslovak Mathematical Journal},
pages = {549--562},
year = {1995},
volume = {45},
number = {3},
doi = {10.21136/CMJ.1995.128532},
mrnumber = {1344520},
zbl = {0852.26010},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1995.128532/}
}
TY - JOUR AU - Faure, Claude-Alain TI - A descriptive definition of some multidimensional gauge integrals JO - Czechoslovak Mathematical Journal PY - 1995 SP - 549 EP - 562 VL - 45 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1995.128532/ DO - 10.21136/CMJ.1995.128532 LA - en ID - 10_21136_CMJ_1995_128532 ER -
%0 Journal Article %A Faure, Claude-Alain %T A descriptive definition of some multidimensional gauge integrals %J Czechoslovak Mathematical Journal %D 1995 %P 549-562 %V 45 %N 3 %U http://geodesic.mathdoc.fr/articles/10.21136/CMJ.1995.128532/ %R 10.21136/CMJ.1995.128532 %G en %F 10_21136_CMJ_1995_128532
Faure, Claude-Alain. A descriptive definition of some multidimensional gauge integrals. Czechoslovak Mathematical Journal, Tome 45 (1995) no. 3, pp. 549-562. doi: 10.21136/CMJ.1995.128532
[1] C.-A. Faure, J. Mawhin: The Hake’s property for some integrals over multidimensional intervals. Preprint (1994). | MR
[2] J. Jarník, J. Kurzweil: Pfeffer integrability does not imply $\text{M}_{1}$-integrability. Czech. Math. J. 44 (1994), 47–56. | MR
[3] J. Jarník, J. Kurzweil, S. Schwabik: On Mawhin’s approach to multiple nonabsolutely convergent integral. Casopis Pest. Mat. 108 (1983), 356–380. | MR
[4] W. B. Jurkat, R. W. Knizia: A characterization of multi-dimensional Perron integrals and the fundamental theorem. Can. J. Math. 43 (1991), 526–539. | DOI | MR
[5] W. B. Jurkat, R. W. Knizia: Generalized absolutely continuous interval functions and multi-dimensional Perron integration. Analysis 12 (1992), 303–313. | DOI | MR
[6] J. Kurzweil, J. Jarník: Equiintegrability and controlled convergence of Perron-type integrable functions. Real Anal. Exchange 17 (1991–92), 110–139. | MR
[7] J. Kurzweil, J. Jarník: Differentiability and integrability in $n$ dimensions with respect to $\alpha $-regular intervals. Results Math. 21 (1992), 138–151. | DOI | MR
[8] J. Kurzweil, J. Jarník: Equivalent definitions of regular generalized Perron integral. Czech. Math. J. 42 (1992), 365–378. | MR
[9] J. Mawhin: Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields. Czech. Math. J. 31 (1981), 614–632. | MR | Zbl
[10] J. Mawhin: Analyse. De Boeck, 1992. | MR | Zbl
[11] D. J. F. Nonnenmacher: Every $\text{M}_{1}$-integrable function is Pfeffer integrable. Czech. Math. J. 43 (1993), 327–330. | MR
[12] D. J. F. Nonnenmacher: A descriptive, additive modification of Mawhin’s integral and the divergence theorem with singularities. Preprint (1993). | MR
[13] W. F. Pfeffer: A Riemann-type integration and the fundamental theorem of calculus. Rend. Circ. Mat. Palermo, Ser. II 36 (1987), 482–506. | DOI | MR | Zbl
[14] W. F. Pfeffer: The divergence theorem. Trans. Amer. Math. Soc. 295 (1986), 665–685. | DOI | MR | Zbl
[15] S. Saks: Theory of the Integral. Hafner Publishing Company, 1937. | Zbl
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