Optimal and Better Transport Plans

@inproceedings{Beiglbck2008OptimalAB,
  title={Optimal and Better Transport Plans},
  author={Mathias Beiglb{\"o}ck and Martin Goldstern and Gabriel Maresch and Walter Schachermayer},
  year={2008}
}
We consider the Monge-Kantorovich 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 may possibly attain the value∞. We show that this is true in a more general setting, in particular for merely Borel measurable cost functions provided that {c… CONTINUE READING

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