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An axiomatic theory of non-absolutely convergent integrals in \(\mathbb{R}^ n\). (English) Zbl 0824.26007

An axiomatic approach is introduced in the theory of non-absolutely convergent integrals for functions of several variables. The obtained integrals are of the type recently introduced by Mawhin, Jarník, Kurzweil, Schwabik, Pfeffer, Jurkat and others. The linearity, restriction and extension, and positivity and uniqueness properties are proved, as well as a fundamental theorem (relation with the indefinite integral), a Saks-Henstock lemma and a transformation formula. Concrete theories will be deduced in a subsequent paper.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
26A39 Denjoy and Perron integrals, other special integrals
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