کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4591807 1335054 2009 21 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Optimal and better transport plans
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Optimal and better transport plans
چکیده انگلیسی

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=∞} is the union of a closed set and a negligible 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 that transport plans are strongly c-monotone if and only if they satisfy a “better” notion of optimality called robust optimality.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Functional Analysis - Volume 256, Issue 6, 15 March 2009, Pages 1907-1927