Optimal and better transport plans II

  • Date: 06/26/2008

Professor Walter Schachermayer (Vienna University of Technology)


University of British Columbia


We consider the Monge-Kantorovick transport problem in a
purely measure theoretic setting, i.e. without imposing continuity
assumptions on the cost function. It is known that transport plans which are concentrated on c-monotone sets are optimal, provided the cost function c is either lower semi-continuous and finite, or continuous and possibly attain infinity. We show that this is true in a more general
setting, in particular for merely Borel measurable cost functions which
are finite almost everywhere on an open set. In a previous paper
Schachermayer and Teichmann considered strongly c-monotone transport plans and proved that every strongly c-monotone transport plan is optimal. We establish necessary and sufficient conditions on c-monotone transport plans to be strongly c-monotone.

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Location: WMAX 110


PIMS Distinguished Lecturer


Note: The paper is on line at http://arxiv.org/abs/0802.0646.