# A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

Annales Polonici Mathematici (1994)

- Volume: 59, Issue: 1, page 85-98
- ISSN: 0066-2216

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topDirk Jens F. Nonnenmacher. "A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities." Annales Polonici Mathematici 59.1 (1994): 85-98. <http://eudml.org/doc/262524>.

@article{DirkJensF1994,

abstract = {Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.},

author = {Dirk Jens F. Nonnenmacher},

journal = {Annales Polonici Mathematici},

keywords = {Mawhin's integral; additive interval function; divergence theorem; divergence of vector fields},

language = {eng},

number = {1},

pages = {85-98},

title = {A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities},

url = {http://eudml.org/doc/262524},

volume = {59},

year = {1994},

}

TY - JOUR

AU - Dirk Jens F. Nonnenmacher

TI - A descriptive, additive modification of Mawhin's integral and the Divergence Theorem with singularities

JO - Annales Polonici Mathematici

PY - 1994

VL - 59

IS - 1

SP - 85

EP - 98

AB - Modifying Mawhin's definition of the GP-integral we define a well-behaved integral over n-dimensional compact intervals. While its starting definition is of Riemann type, we also establish an equivalent descriptive definition involving characteristic null conditions. This characterization is then used to obtain a quite general form of the divergence theorem.

LA - eng

KW - Mawhin's integral; additive interval function; divergence theorem; divergence of vector fields

UR - http://eudml.org/doc/262524

ER -

## References

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- [Ju-No] W. B. Jurkat and D. J. F. Nonnenmacher, A generalized n-dimensional Riemann integral and the Divergence Theorem with singularities, Acta Sci. Math. (Szeged), to appear. Zbl0810.26007
- [Ku-Jar1] J. Kurzweil and J. Jarník, Equivalent definitions of regular generalized Perron integral, Czechoslovak Math. J. 42 (117) (1992), 365-378. Zbl0782.26004
- [Ku-Jar2] J. Kurzweil and J. Jarník, Differentiability and integrability in n dimensions with respect to α-regular intervals, Results Math. 21 (1992), 138-151. Zbl0764.28005
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- [Maw] J. Mawhin, Generalized multiple Perron integrals and the Green-Goursat theorem for differentiable vector fields, Czechoslovak Math. J. 31 (106) (1981), 614-632. Zbl0562.26004
- [No] D. J. F. Nonnenmacher, Every M₁-integrable function is Pfeffer integrable, Czechoslovak Math. J. 43 (118) (1993), 327-330. Zbl0789.26006
- [Pf] W. F. Pfeffer, The divergence theorem, Trans. Amer. Math. Soc. 295 (1986), 665-685. Zbl0596.26007
- [Saks] S. Saks, Theory of the Integral, Dover, New York, 1964.

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