A mean value theorem for metric spaces |
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| Authors: | P M Carvalho Neto P A Liboni Filho |
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| Affiliation: | 1. Instituto de Matemática, Estatística e Computa??o Científica, Universidade Estadual de Campinas, Rua, Campinas, Brazil;2. +55 16 3306 6727+55 16 3306 6727;3. Universidade Federal de S?o Carlos, Departamento de Matemática, Carlos, Brazil |
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| Abstract: | We present a form of the Mean Value Theorem (MVT) for a continuous function f between metric spaces, connecting it with the possibility to choose the  relation of f in a homeomorphic way. We also compare our formulation of the MVT with the classic one when the metric spaces are open subsets of Banach spaces. As a consequence, we derive a version of the Mean Value Propriety for measure spaces that also possesses a compatible metric structure. |
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| Keywords: | Metric space mean value property/theorem homeomorphism average of functions Primary: 54E40 30L99 Secondary: 26A15 26E40 |
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