Geodesic
An Analytic Characterization of Independence and Markov Type Dependence
Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 4, pp. 422-426

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In this article it is proved that a functional dependence between the probabilities for intersections of outcomes of trials and the probabilities for the outcomes themselves can exist (all the exceptions are listed) only provided the trials are independent. A similar result is established for measures, which are Markov with respect to an arbitrarily regular complex. 
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     author = {N. N. Vorob'ev},
     title = {An {Analytic} {Characterization} of {Independence} and {Markov} {Type} {Dependence}},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
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     year = {1961},
     language = {ru},
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N. N. Vorob'ev. An Analytic Characterization of Independence and Markov Type Dependence. Teoriâ veroâtnostej i ee primeneniâ, Tome 6 (1961) no. 4, pp. 422-426. http://geodesic.mathdoc.fr/item/TVP_1961_6_4_a2/