| Title:
|
A descriptive definition of some multidimensional gauge integrals (English) |
| Author:
|
Faure, Claude-Alain |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
45 |
| Issue:
|
3 |
| Year:
|
1995 |
| Pages:
|
549-562 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A39 |
| MSC:
|
26B20 |
| idZBL:
|
Zbl 0852.26010 |
| idMR:
|
MR1344520 |
| DOI:
|
10.21136/CMJ.1995.128532 |
| . |
| Date available:
|
2009-09-24T09:50:32Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128532 |
| . |
| Reference:
|
[1] C.-A. Faure, J. Mawhin: The Hake’s property for some integrals over multidimensional intervals.Preprint (1994). MR 1348084 |
| Reference:
|
[2] J. Jarník, J. Kurzweil: Pfeffer integrability does not imply $\text{M}_{1}$-integrability.Czech. Math. J. 44 (1994), 47–56. MR 1257935 |
| Reference:
|
[3] J. Jarník, J. Kurzweil, S. Schwabik: On Mawhin’s approach to multiple nonabsolutely convergent integral.Casopis Pest. Mat. 108 (1983), 356–380. MR 0727536 |
| Reference:
|
[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. MR 1118008, 10.4153/CJM-1991-032-8 |
| Reference:
|
[5] W. B. Jurkat, R. W. Knizia: Generalized absolutely continuous interval functions and multi-dimensional Perron integration.Analysis 12 (1992), 303–313. MR 1182631, 10.1524/anly.1992.12.34.303 |
| Reference:
|
[6] J. Kurzweil, J. Jarník: Equiintegrability and controlled convergence of Perron-type integrable functions.Real Anal. Exchange 17 (1991–92), 110–139. MR 1147361 |
| Reference:
|
[7] J. Kurzweil, J. Jarník: Differentiability and integrability in $n$ dimensions with respect to $\alpha $-regular intervals.Results Math. 21 (1992), 138–151. MR 1146639, 10.1007/BF03323075 |
| Reference:
|
[8] J. Kurzweil, J. Jarník: Equivalent definitions of regular generalized Perron integral.Czech. Math. J. 42 (1992), 365–378. MR 1179506 |
| Reference:
|
[9] J. Mawhin: Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields.Czech. Math. J. 31 (1981), 614–632. Zbl 0562.26004, MR 0631606 |
| Reference:
|
[10] J. Mawhin: Analyse.De Boeck, 1992. Zbl 0759.26004, MR 1190926 |
| Reference:
|
[11] D. J. F. Nonnenmacher: Every $\text{M}_{1}$-integrable function is Pfeffer integrable.Czech. Math. J. 43 (1993), 327–330. MR 1211754 |
| Reference:
|
[12] D. J. F. Nonnenmacher: A descriptive, additive modification of Mawhin’s integral and the divergence theorem with singularities.Preprint (1993). MR 1270304 |
| Reference:
|
[13] W. F. Pfeffer: A Riemann-type integration and the fundamental theorem of calculus.Rend. Circ. Mat. Palermo, Ser. II 36 (1987), 482–506. Zbl 0669.26007, MR 0981151, 10.1007/BF02844902 |
| Reference:
|
[14] W. F. Pfeffer: The divergence theorem.Trans. Amer. Math. Soc. 295 (1986), 665–685. Zbl 0596.26007, MR 0833702, 10.1090/S0002-9947-1986-0833702-0 |
| Reference:
|
[15] S. Saks: Theory of the Integral.Hafner Publishing Company, 1937. Zbl 0017.30004 |
| . |
