Decomposition of ranges of vector measures

Abraham Neyman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

8 Scopus citations

Abstract

The following conditions on a zonoid Z, i.e., a range of a non-atomic vector measure, are equivalent: (i) the extreme set containing 0 in its relative interior is a parallelepiped; (ii) the zonoid Z determines the m-range of any non-atomic vector measure with range Z, where the m-range of a vector measure μ is the set of m-tuples (μ(S 1), ..., μ(S m), where S 1, ...S m are disjoint measurable sets and (iii) there is avector measure space (X, Σ, μ) such that any finite factorization of Z, Z =ΣZ i, in the class of zonoids could be achieved by decomposing (X, Σ). In the case of ranges of non-atomic probability measures (i) is automatically satisfied, so (ii) and (iii) hold.

Original languageEnglish
Pages (from-to)54-64
Number of pages11
JournalIsrael Journal of Mathematics
Volume40
Issue number1
DOIs
StatePublished - Mar 1981

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