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A Riemann type integration and the fundamental theorem of calculus. (English) Zbl 0669.26007
This expository paper proposes a self-contained presentation of a recent approach to a Riemann type integral on differentiable manifolds which can integrate the exterior derivative of any differentiable form and gives the result of the classical Stokes formula. This approach is a development of the work of Kurzweil and Henstock providing a Riemann-like definition of Perron’s integral on the line and of subsequent n- dimensional extensions by the reviewer, JarnĂ­k, Kurzweil, Schwabik and the author. Those (related) approaches are compared and discussed in his clearly written paper which ends with an interesting list of open problems.
Reviewer: J.Mawhin

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