| Title:
|
The fundamental theorem for the $\nu_1$-integral on more general sets and a corresponding divergence theorem with singularities (English) |
| Author:
|
Jurkat, W. B. |
| Author:
|
Nonnenmacher, D. J. F. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
45 |
| Issue:
|
1 |
| Year:
|
1995 |
| Pages:
|
69-77 |
| . |
| Category:
|
math |
| . |
| MSC:
|
26A39 |
| MSC:
|
26B20 |
| idZBL:
|
Zbl 0832.26008 |
| idMR:
|
MR1314531 |
| DOI:
|
10.21136/CMJ.1995.128511 |
| . |
| Date available:
|
2009-09-24T09:44:37Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/128511 |
| . |
| Reference:
|
[Fed] H. Federer: Geometric Measure Theory.Springer, New York, 1969. Zbl 0176.00801, MR 0257325 |
| Reference:
|
[Jar-Ku 1] J. Jarnik and J. Kurzweil: A non-absolutely convergent integral which admits $C^1$-Transformations.Časopis pro Pěstovaní Mat. 109 (1984), 157–167. MR 0744873 |
| Reference:
|
[Jar-Ku 2] J. Jarnik 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:
|
[Jar-Ku 3] J. Jarnik and J. Kurzweil: A new and more powerful concept of the $PU$-integral.Czech. Math. J. 38 (113) (1988), 8–48. MR 0925939 |
| Reference:
|
[Ju] W.B. Jurkat: The Divergence Theorem and Perron integration with exceptional sets.Czech. Math. J. 43 (1993), 27–45. Zbl 0789.26005, MR 1205229 |
| Reference:
|
[Ju-No 1] W.B. Jurkat and D.J.F. Nonnenmacher: An axiomatic theory of non-absolutely convergent integrals in $R^n$.Fund. Math. 145 (1994), 221–242. MR 1297406, 10.4064/fm-145-3-221-242 |
| Reference:
|
[Ju-No 2] W.B. Jurkat and D.J.F. Nonnenmacher: A generalized $n$-dimensional Riemann integral and the Divergence Theorem with singularities.Acta Sci. Math. (Szeged) 59 (1994), 241–256. MR 1285443 |
| Reference:
|
[No] D.J.F. Nonnenmacher: Theorie mehrdimensionaler Perron-Integrale mit Ausnahmemengen.PhD thesis, Univ. of Ulm, 1990. Zbl 0724.26010 |
| Reference:
|
[Pf 1] 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:
|
[Pf 2] W.F. Pfeffer: The Gauß-Green Theorem.Advances in Mathematics 87 (1991), no. 1, 93–147. Zbl 0732.26013, MR 1102966, 10.1016/0001-8708(91)90063-D |
| Reference:
|
[Saks] S. Saks: Theory of the integral.Dover, New York, 1964. MR 0167578 |
| . |
