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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, Jarník, 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.)
Full Text:
##### References:
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