The Monge Problem in Banach Spaces |
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Authors: | Henri Heinich |
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Institution: | (1) Département de Génie Mathématique, INSA de Rouen, place E. Blondel, 76131 Mont-Saint-Aignan Cedex, France |
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Abstract: | In this paper, we generalize the Kantorovich functional to K?the-spaces for a cost or a profit function. We examine the convergence
of probabilities with respect to this functional for some K?the-spaces. We study the Monge problem: Let
be a K?the-space, P and Q two Borel probabilities defined on a Polish space M and a cost function
. A K?the functional
is defined by
(P, Q) = inf
where
is the law of X. If c is a profit function, we note
. (P, Q) = sup
Under some conditions, we show the existence of a Monge function, φ, such that
, or
.
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Keywords: | Cost and profit functions Monge– Kantorovich transportation problem Monge problem optimal coupling K?the and Orlicz spaces |
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