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Measures on two-dimensional products
Published online by Cambridge University Press: 26 February 2010
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§1. Introduction. Let two probability spaces (X, , μ,) and (Y, ℬ, ν) be given. For a subset D of X × Y and a real number d ≥ 0 we consider the following problem
(MP) Does there exist a measure » on X × Y having μ and ν as marginals and such that λ (D) ≥ 1 − d?
This problem comes from Strassen's paper [12], where Borel probabilities on Polish spaces were treated. Further, it was investigated by many authors in more general settings (cf. [2], [4]-[7], [11]-[13]).
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