On the Role of Cylindrical Functions in Kantorovich duality
Abstract
We study the dual formulation of the Monge-Kantorovich optimal transportation problem, in particular under what circumstances it is permitted in an infinite dimensional setting to use cylindrical functions, i.e. functions of the form P where P is a finite-rank operator and is a smooth, compactly supported function. In the last section, some examples of applications are presented.
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