Decomposition of ranges of vector measures |
| |
Authors: | Abraham Neyman |
| |
Institution: | (1) The Institute for Advanced Studies, The Hebrew University of Jerusalem, Mount Scopus, Jerusalem, Israel;(2) Department of Mathematics, University of California, Berkeley, Berkeley, California, USA |
| |
Abstract: | The following conditions on a zonoidZ, 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 zonoidZ determines them-range of any non-atomic vector measure with rangeZ, where them-range of a vector measure μ is the set ofm-tuples (μ(S
1), …, μ(S
m), whereS
1, …S
m
are disjoint measurable sets and (iii) there is avector measure space (X, Σ, μ) such that any finite factorization ofZ, 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.
Partially supported by NSF grant MCS-79-06634 |
| |
Keywords: | |
本文献已被 SpringerLink 等数据库收录! |
|