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A pre-hilbert space consisting of classes of convex sets

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Abstract

An equivalence relation is defined in the set of all bounded closed convex sets in Euclidean spaceE n. The equivalence classes are shown to be elements of a pre-Hilbert spaceA n, and geometrical relationships betweenA n andE n are investigated.

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References

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Authors and Affiliations

  1. University of Birmingham, England

    G. C. Shephard

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  1. G. C. Shephard
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Shephard, G.C. A pre-hilbert space consisting of classes of convex sets. Israel J. Math. 4, 1–10 (1966). https://doi.org/10.1007/BF02760065

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  • DOI: https://doi.org/10.1007/BF02760065

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