# An axiomatic theory of non-absolutely convergent integrals in Rn

Fundamenta Mathematicae (1994)

- Volume: 145, Issue: 3, page 221-242
- ISSN: 0016-2736

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topJurkat, W., and Nonnenmacher, D.. "An axiomatic theory of non-absolutely convergent integrals in Rn." Fundamenta Mathematicae 145.3 (1994): 221-242. <http://eudml.org/doc/212044>.

@article{Jurkat1994,

abstract = {We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.},

author = {Jurkat, W., Nonnenmacher, D.},

journal = {Fundamenta Mathematicae},

keywords = {generalized Riemann integral; divergence theorem; non-absolutely convergent integrals; Saks-Henstock lemma},

language = {eng},

number = {3},

pages = {221-242},

title = {An axiomatic theory of non-absolutely convergent integrals in Rn},

url = {http://eudml.org/doc/212044},

volume = {145},

year = {1994},

}

TY - JOUR

AU - Jurkat, W.

AU - Nonnenmacher, D.

TI - An axiomatic theory of non-absolutely convergent integrals in Rn

JO - Fundamenta Mathematicae

PY - 1994

VL - 145

IS - 3

SP - 221

EP - 242

AB - We introduce an axiomatic approach to the theory of non-absolutely convergent integrals. The definition of our ν-integral will be descriptive and depends mainly on characteristic null conditions. By specializing our concepts we will later obtain concrete theories of integration with natural properties and very general versions of the divergence theorem.

LA - eng

KW - generalized Riemann integral; divergence theorem; non-absolutely convergent integrals; Saks-Henstock lemma

UR - http://eudml.org/doc/212044

ER -

## References

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- [No] D. J. F. Nonnenmacher, Theorie mehrdimensionaler Perron-Integrale mit Ausnahmemengen, PhD thesis, Univ. of Ulm, 1990. Zbl0724.26010
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- [Pf 2] W. F. Pfeffer, The Gauß-Green Theorem, Adv. in Math. 87 (1991), 93-147. Zbl0732.26013
- [Pf 3] W. F. Pfeffer, A descriptive definition of a variational integral and applications, Indiana Univ. Math. J. 40 (1991), 259-270. Zbl0747.26010
- [Pf-Ya] W. F. Pfeffer and W.-C. Yang, A multidimensional variational integral and its extensions, Real Anal. Exchange 15 (1989-1990), 111-169.
- [Rot] J. J. Rotman, An Introduction to Algebraic Topology, Graduate Texts in Math., Springer, 1988.
- [Saks] S. Saks, Theory of the Integral, Dover, New York, 1964.
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## Citations in EuDML Documents

top- Wolfgang B. Jurkat, D. J. F. Nonnenmacher, A Hake-type property for the ${\nu}_{1}$-integral and its relation to other integration processes
- Wolfgang B. Jurkat, D. J. F. Nonnenmacher, The fundamental theorem for the ${\nu}_{1}$-integral on more general sets and a corresponding divergence theorem with singularities
- W. Jurkat, D. Nonnenmacher, A theory of non-absolutely convergent integrals in Rn with singularities on a regular boundary

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