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An invariant Riemann type integral defined by figures. (English) Zbl 0808.26006

Following the work of Mawhin, Jarník, Kurzweil, Schwabik, and Pfeffer, the authors introduce a generalized Riemann integral of Kurzweil-Henstock type over figures (finite union of intervals), which integrates the divergence of noncontinuously differentiable vector fields. They show that this integral is invariant with respect to lipeomorphisms between figures.

MSC:

26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)
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