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A generalized mean-value theorem

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Abstract

We give another proof of Seymour and Zaslavsky's theorem: For every familyf 1,f 2,...,f n of continous functions defined on [0, 1], there exists a finite setF⊂[0, 1] such that the average sum off k overF coincides with the integral off k for everyk=1, 2,...,n.

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References

  1. Dugundji, J.: Topology. Boston: Allyn and Bacon. 1966.

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  2. Seymour, P. D., Zaslavsky, T.: Averagin sets: a generalization of mean values and spherical designs. Adv. Math.52, 213–240 (1984).

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  1. Facultad de Matemáticas, Universidad de Sevilla, Apdo. 1160, 41080, Sevilla, Spain

    Juan Arias de Reyna

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  1. Juan Arias de Reyna
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de Reyna, J.A. A generalized mean-value theorem. Monatshefte für Mathematik 106, 95–97 (1988). https://doi.org/10.1007/BF01298830

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  • DOI: https://doi.org/10.1007/BF01298830

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