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Distributions and Valuations
Author(s) -
Goodey Paul,
Weil Wolfgang
Publication year - 1984
Publication title -
proceedings of the london mathematical society
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.899
H-Index - 65
eISSN - 1460-244X
pISSN - 0024-6115
DOI - 10.1112/plms/s3-49.3.504
Subject(s) - mathematics , multilinear map , cartesian product , invariant (physics) , product (mathematics) , unit sphere , homogeneous , regular polygon , pure mathematics , product topology , combinatorics , mathematical analysis , geometry , mathematical physics
This paper is concerned with continuous multilinear functions defined on the n ‐fold cartesian product K n , where K denotes the space of non‐empty compact convex subsets of E d . We show that these functions correspond to distributions on the product Ω n , where Ω is the unit ( d − 1)‐sphere. This correspondence is then used to characterize the continuous translation‐invariant valuations on K which are homogeneous of degree 1.