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Duality theorems for marginal problems. (English) Zbl 0535.60002

Given topological spaces \(X_ 1,...,X_ n\) with product space X, probability measures \(\mu_ i\) on \(X_ i\) together with a real function h on X define a marginal problem as well as a dual problem. Using an extended version of G. Choquet’s theorem on capacities [Ann. Inst. Fourier 9, 83-89 (1960; Zbl 0093.297)], an analogue of the classical duality theorem of linear programming is established, imposing only weak conditions on the topology of the spaces \(X_ i\) and the measurability resp. boundedness of the function h. Applications concern, among others, measures with given support, stochastic order and general marginal problems.

MSC:

60A10 Probabilistic measure theory

Citations:

Zbl 0093.297
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References:

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