The fundamental theorem for the ν 1 -integral on more general sets and a corresponding divergence theorem with singularities

Wolfgang B. Jurkat; D. J. F. Nonnenmacher

Czechoslovak Mathematical Journal (1995)

  • Volume: 45, Issue: 1, page 69-77
  • ISSN: 0011-4642

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Jurkat, Wolfgang B., and Nonnenmacher, D. J. F.. "The fundamental theorem for the $\nu _1$-integral on more general sets and a corresponding divergence theorem with singularities." Czechoslovak Mathematical Journal 45.1 (1995): 69-77. <http://eudml.org/doc/31458>.

@article{Jurkat1995,
author = {Jurkat, Wolfgang B., Nonnenmacher, D. J. F.},
journal = {Czechoslovak Mathematical Journal},
keywords = {multidimensional nonabsolute integrals; divergence theorem; vector field},
language = {eng},
number = {1},
pages = {69-77},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {The fundamental theorem for the $\nu _1$-integral on more general sets and a corresponding divergence theorem with singularities},
url = {http://eudml.org/doc/31458},
volume = {45},
year = {1995},
}

TY - JOUR
AU - Jurkat, Wolfgang B.
AU - Nonnenmacher, D. J. F.
TI - The fundamental theorem for the $\nu _1$-integral on more general sets and a corresponding divergence theorem with singularities
JO - Czechoslovak Mathematical Journal
PY - 1995
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 45
IS - 1
SP - 69
EP - 77
LA - eng
KW - multidimensional nonabsolute integrals; divergence theorem; vector field
UR - http://eudml.org/doc/31458
ER -

References

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  1. Geometric Measure Theory, Springer, New York, 1969. (1969) Zbl0176.00801MR0257325
  2. A non-absolutely convergent integral which admits C 1 -Transformations, Časopis pro Pěstovaní Mat. 109 (1984), 157–167. (1984) MR0744873
  3. A non-absolutely convergent integral which admits transformation and can be used for integration on manifolds, Czech. Math. J. 35 (110) (1985), 116–139. (1985) MR0779340
  4. A new and more powerful concept of the P U -integral, Czech. Math. J. 38 (113) (1988), 8–48. (1988) MR0925939
  5. The Divergence Theorem and Perron integration with exceptional sets, Czech. Math. J. 43 (1993), 27–45. (1993) Zbl0789.26005MR1205229
  6. 10.4064/fm-145-3-221-242, Fund. Math. 145 (1994), 221–242. (1994) MR1297406DOI10.4064/fm-145-3-221-242
  7. A generalized n -dimensional Riemann integral and the Divergence Theorem with singularities, Acta Sci. Math. (Szeged) 59 (1994), 241–256. (1994) MR1285443
  8. Theorie mehrdimensionaler Perron-Integrale mit Ausnahmemengen, PhD thesis, Univ. of Ulm, 1990. (1990) Zbl0724.26010
  9. 10.1090/S0002-9947-1986-0833702-0, Trans. Amer. Math. Soc. 295 (1986), 665–685. (1986) Zbl0596.26007MR0833702DOI10.1090/S0002-9947-1986-0833702-0
  10. 10.1016/0001-8708(91)90063-D, Advances in Mathematics 87 (1991), no. 1, 93–147. (1991) Zbl0732.26013MR1102966DOI10.1016/0001-8708(91)90063-D
  11. Theory of the integral, Dover, New York, 1964. (1964) MR0167578

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