- Volume 1, Number 3 (1995), 217-243.
Supports of doubly stochastic measures
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.
Bernoulli, Volume 1, Number 3 (1995), 217-243.
First available in Project Euclid: 29 October 2007
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Hestir, Kevin; Williams, Stanley C. Supports of doubly stochastic measures. Bernoulli 1 (1995), no. 3, 217--243. doi:10.3150/bj/1193667816. https://projecteuclid.org/euclid.bj/1193667816