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Czechoslovak Mathematical Journal, Vol. 59, No. 3, pp. 721-739, 2009
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A simplified multidimensional integral

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Agnes M. Backhausz, Vilmos Komornik, Tivadar Szilagyi

* Agnes M. Backhausz*, Institute of Mathematics, Eotvos Lorand University, Pazmany P. setany 1/C, 1117 Budapest, Hungary, e-mail: ` agnes@cs.elte.hu`; * Vilmos Komornik*, Departement de mathematique, Universite Louis Pasteur, 7 rue Rene Descartes, 67084 Strasbourg Cedex, France, e-mail: ` komornik@math.u-strasbg.fr`; * Tivadar Szilagyi*, Department of Applied Analysis and Computational Mathematics, Eotvos Lorand University, Pazmany P. setany 1/C, 1117 Budapest, Hungary, e-mail: ` sztiv@cs.elte.hu`

**Abstract:** We present a simplified integral of functions of several variables. Although less general than the Riemann integral, most functions of practical interest are still integrable. On the other hand, the basic integral theorems can be obtained more quickly. We also give a characterization of the integrable functions and their primitives.

**Keywords:** integral of several variables, characterization of primitives

**Classification (MSC 2000):** 26B15, 28A10

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