Continuity and representation of valuations on star bodies

It is shown that every continuous valuation defined on n-dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly continuous on bounded sets. We also characterize continuous valuatio...

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Bibliographic Details
Published inAdvances in mathematics (New York. 1965) Vol. 329; pp. 361 - 391
Main Authors Tradacete, Pedro, Villanueva, Ignacio
Format Journal Article
LanguageEnglish
Published Elsevier Inc 30.04.2018
Subjects
Star bodies
Star sets
Valuations
Star bodies
Star sets
52A30
52B45
Valuations
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Summary:It is shown that every continuous valuation defined on n-dimensional star bodies has an integral representation in terms of the radial function. Our argument is based on the non-trivial fact that continuous valuations are uniformly continuous on bounded sets. We also characterize continuous valuations on the n-dimensional star bodies that arise as restriction of a measure on Rn.
ISSN:0001-8708
1090-2082
DOI:10.1016/j.aim.2018.02.021