Open Access
September 1995 Supports of doubly stochastic measures
Kevin Hestir, Stanley C. Williams
Bernoulli 1(3): 217-243 (September 1995). DOI: 10.3150/bj/1193667816


Recent work has shown that extreme doubly stochastic measures are supported on sets that have no axial cycles. We give a new proof of this result and examine the supporting set structure more closely. It is shown that the property of no axial cycles leads to a tree-like structure which naturally partitions the support into a collection of disjoint graphs of functions from the x-axis to the y-axis and from the y-axis to the x-axis. These functions are called a limb numbering system. It is shown that if the disjoint graphs in the limb numbering system are measurable, then the supporting set supports a unique doubly stochastic measure. Further, the limb structure can be used to develop a general method for constructing sets which support a unique doubly stochastic measure.


Download Citation

Kevin Hestir. Stanley C. Williams. "Supports of doubly stochastic measures." Bernoulli 1 (3) 217 - 243, September 1995.


Published: September 1995
First available in Project Euclid: 29 October 2007

zbMATH: 0844.60002
MathSciNet: MR1363539
Digital Object Identifier: 10.3150/bj/1193667816

Keywords: extreme point , Sets of uniqueness

Rights: Copyright © 1995 Bernoulli Society for Mathematical Statistics and Probability

Vol.1 • No. 3 • September 1995
Back to Top