Integration by Means of Riemann Sums in Banach Spaces I
Wolfgang Erben
Hochschule für Technik Stuttgart, GermanyGerhard Grimeisen
Universität Stuttgart, Germany
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Abstract
In 1938, G. Birkhoff [2] developed a theory of integration in Banach spaces which uses the approach via modified Riemann sums. In our paper, we generalize Birkhoff’s integration by basing it on an arbitrary set of "-partitions" (being directed in a natural way) instead of the set of all "-partitions" of the underlying measure space . Our technique of working with infinite Riemann sums and limits of filtered families of such sums takes advantage of the 1-point completions of certain partial universal algebras as discussed by G. Grimeisen in [13].
Cite this article
Wolfgang Erben, Gerhard Grimeisen, Integration by Means of Riemann Sums in Banach Spaces I. Z. Anal. Anwend. 9 (1990), no. 6, pp. 481–501
DOI 10.4171/ZAA/419