A generalisation to Birkhoff - von Neumann theorem

  title={A generalisation to Birkhoff - von Neumann theorem},
  author={Liviu Paunescu and Florin Radulescu},
  journal={arXiv: Functional Analysis},
The classic Birkhoff- von Neumann theorem states that the set of doubly stochastic matrices is the convex hull of the permutation matrices. In this paper, we study a generalisation of this theorem in the type $II_1$ setting. Namely, we replace a doubly stochastic matrix with a collection of measure preserving partial isomorphisms, of the unit interval, with similar properties. We show that a weaker version of this theorem still holds. 
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