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Banach limit in convexity and geometric means for convex bodies

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  • In this note we construct Banach limits on the class of sequences of convex bodies. Surprisingly, the construction uses the recently introduced geometric mean of convex bodies. In the opposite direction, we explain how Banach limits can be used to construct a new variant of the geometric mean that has some desirable properties.
    Mathematics Subject Classification: 52A20, 46A22.


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