MATHEMATICA BOHEMICA, Vol. 121, No. 4, pp. 425-447, 1996

Abstract Perron-Stieltjes integral

Stefan Schwabik

Stefan Schwabik, Mathematical Institute, Academy of Sciences, Zitna 25, 115 67 Praha 1, Czech Republic, e-mail:

Abstract: Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces are presented. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums. It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Ch. S. Honig presented a Stieltjes integral for Banach space valued functions. For Honig's integral the Dushnik interior integral presents the background. \endgraf It should be mentioned that abstract Stieltjes integration was recently used by O. Diekmann, M. Gyllenberg and H. R. Thieme for describing the behaviour of some evolutionary systems originating in problems concerning structured population dynamics.

Keywords: bilinear triple, Perron-Stieltjes integral

Classification (MSC91): 28B05

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