A Riemann type integration and the fundamental theorem of calculus
type: Item
instance of: scholarly article
title: A Riemann type integration and the fundamental theorem of calculus
zbMATH Open document ID: 0669.26007
DOI: 10.1007/BF02844902
author: Washek F. Pfeffer
publication date: 1987-01-01T00:00:00Z
review text: 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.
Mathematics Subject Classification ID: 26B20
zbMATH DE Number: 4095807
zbMATH Keywords: Stokes theorem
zbMATH Keywords: nonabsolute integrals
zbMATH Keywords: Riemann sums
zbMATH Keywords: Riemann type integral on differentiable manifolds
zbMATH Keywords: Stokes formula
reviewed by: Jean Mawhin
MaRDI profile type: Publication
cites work: Q5565773
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published in: Rendiconti del Circolo Matematico di Palermo
description: scientific article; zbMATH DE number 4095807