| Title:
|
The divergence theorem and Perron integration with exceptional sets (English) |
| Author:
|
Jurkat, Wolfgang B. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
1993 |
| Pages:
|
27-45 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A39 |
| MSC:
|
26B20 |
| idZBL:
|
Zbl 0789.26005 |
| idMR:
|
MR1205229 |
| DOI:
|
10.21136/CMJ.1993.128388 |
| . |
| Date available:
|
2009-09-24T09:27:05Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128388 |
| . |
| Reference:
|
[1] H. Bauer: Der Perronsche Integralbegriff und seine Beziehung zum Lebesgueschen.Monatsh. Math. 26 (1915), 153–198. MR 1548647, 10.1007/BF01999447 |
| Reference:
|
[2] H. Federer: Geometric Measure Theory.Springer, Berlin-Heidelberg-New-York, 1969. Zbl 0176.00801, MR 0257325 |
| Reference:
|
[3] J.Jarník, J. Kurzweil, Š. Schwabik: On Mawhin’s approach to multiple non-absolutely convergent integrals.Časopis pro Pěst. Mat. 108 (4) (1983), 356–380. MR 0727536 |
| Reference:
|
[4] J. Jarník and J. Kurzweil: A non-absolutely convergent integral which admits $C^1$-transformations.Casopis pro Pest. Mat. 109 (1984), 157–167. MR 0744873 |
| Reference:
|
[5] J. Jarník and J. Kurzweil: A non-absolutely convergent integral which admits transformation and can be used for integration on manifolds.Czech. Math. J. 35 (110) (1985), 116–139. MR 0779340 |
| Reference:
|
[6] J. Jarník and J. Kurzweil: A new and more powerful concept of the PU-integral.Czech. Math. J. 38 (113) (1988), 8–48. MR 0925939 |
| Reference:
|
[7] W.B. Jurkat and R.W. Knizia: A characterization of multi-dimensional Perron integrals and the Fundamental Theorem.(to appear). MR 1118008 |
| Reference:
|
[8] W.B. Jurkat and R.W. Knizia: Generalized absolutely continuous interval functions and multi-dimensional Perron integration.(to appear). MR 1182631 |
| Reference:
|
[9] W.B. Jurkat and D.J.F. Nonnenmacher: The general form of Green’s Theorem.(to appear). MR 1000158 |
| Reference:
|
[10] K. Karták and J. Mařík: A non-absolutely convergent integral in $E_m$ and the theorem of Gauss.Czech. Math. J. 15 (90) (1965), 253–259. MR 0177092 |
| Reference:
|
[11] J. Mařík: The surface integral.Czech. Math. J. 6 (81) (1956), 522–558. MR 0089891 |
| Reference:
|
[12] J. Mawhin: Generalized Riemann integral and the divergence theorem for differentiable vector fields.Proceedings of the International Christoffel Symposium, Birkhaeuser, Basel, 1981, pp. 704–714. MR 0661109 |
| Reference:
|
[13] J. Mawhin: Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields.Czech. Math. J. 31 (106) (1981), 614–632. Zbl 0562.26004, MR 0631606 |
| Reference:
|
[14] D.J.F. Nonnenmacher: Perron Integration auf allgemeinen Bereichen und der Satz von Gree.Diplomarbeit Univ. Ulm, 1988, pp. 1–117. |
| Reference:
|
[15] W.F. Pfeffer: The divergence theorem.Trans. AMS 295 (1986), 665–685. Zbl 0596.26007, MR 0833702, 10.1090/S0002-9947-1986-0833702-0 |
| Reference:
|
[16] W.F. Pfeffer: The multidimensional fundamental theorem of calculus.J. Austral. Math. Soc. 43 (1987), 143–170. Zbl 0638.26011, MR 0896622, 10.1017/S1446788700029293 |
| Reference:
|
[17] W.F. Pfeffer and W.-C. Yang: A multidimensional variational integral and its extensions.preprint (1988). MR 1042534 |
| Reference:
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[18] S. Saks: Theory of the Integral ($2^{\text{nd}}$ revised edition).Dover Publications, New-York, 1964. MR 0167578 |
| Reference:
|
[19] V.L. Shapiro: On Green’s theorem.J. London Math. Soc. 32 (1957), 261–269. Zbl 0079.27902, MR 0089275, 10.1112/jlms/s1-32.3.261 |
| . |
