A generalization of the set averaging theorem |
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Authors: | G M Ivanov E S Polovinkin |
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Institution: | 1. Moscow Institute of Physics and Technology, Moscow, Russia
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Abstract: | We consider the possibility of generalizing the averaging theorem from the case of sets from n-dimensional Euclidean space to the case of sets from Banach spaces. The result is a cornerstone for constructing the theory of the Riemann integral for non-convex-valued multivalued mappings and for proving the convexity of this multivalued integral. We obtain a generalization of the averaging theorem to the case of sets from uniformly smooth Banach spaces as well as some corollaries. |
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