Continuity and representation of valuations on star bodies. Articles uri icon

authors

  • TRADACETE PEREZ, PEDRO
  • VILLANUEVA DIEZ, IGNACIO

publication date

  • April 2018

start page

  • 361

end page

  • 391

volume

  • 329

International Standard Serial Number (ISSN)

  • 0001-8708

Electronic International Standard Serial Number (EISSN)

  • 1090-2082

abstract

  • 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.

keywords

  • star sets; star bodies; valuations