- ADVANCES IN MATHEMATICS Journal
- April 2018
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- 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 R-n. (C) 2018 Elsevier Inc. All rights reserved.
- star sets; star bodies; valuations