Birkhoff's theorem for a family of probability spaces
arXiv:math/0512451
Abstract
The paper extends Birkhoff's theorem on doubly stochastic matrices to some countable families of discrete probability spaces with nonempty intersections. We join every two elements lying in the same probability space by an edge and formulate our results in terms of the obtained graph.
20 pages; to appear in "St Petersburg Mathematical Journal", vol. 17, No. 5. See also http://www.mth.kcl.ac.uk/~ysafarov/Publications/index.html