Geodesic
Computable measures coprojection consistent with ordering relation is not necessarily computable
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2012), pp. 17-20

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An example of two computable probabilistic measures is given on infinite binary sequences such that the two measures are comparable (there exists their coupling that forbids the pairs of symbols with the first member less than the second one), but all such couplings are incomputable. 
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     author = {M. A. Raskin},
     title = {Computable measures coprojection consistent with ordering relation is not necessarily computable},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
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     publisher = {mathdoc},
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     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2012_2_a3/}
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M. A. Raskin. Computable measures coprojection consistent with ordering relation is not necessarily computable. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 2 (2012), pp. 17-20. http://geodesic.mathdoc.fr/item/VMUMM_2012_2_a3/