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Let and be two compact spaces endowed with
respective measures and satisfying the condition . Let be a continuous function on the product space . The mass transfer problem consists in determining a measure on
whose marginals coincide with and , and such that
the total cost be minimized. We first
show that if the cost function is decomposable, i.e., can be
represented as the sum of two continuous functions defined on and
, respectively, then every feasible measure is optimal. Conversely,
when...
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