Geodesic
Many-valued measure-preserving mappings (polymorphisms) and Markovian operators
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 26-61

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Systematic presentation of the basic concept of the theory of many-valued measure-preserving mappings of spaces and their functional equivalents – Markov operators. Relationship with Markov processes and dilations, with exact endomorphisms; extremal and indecomposable mappings; factor mappings; bistochastic and quasibistochastic measures; examples and applications. 
@article{ZNSL_1977_72_a1,
     author = {A. M. Vershik},
     title = {Many-valued measure-preserving mappings (polymorphisms) and {Markovian} operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {26--61},
     publisher = {mathdoc},
     volume = {72},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a1/}
}
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A. M. Vershik. Many-valued measure-preserving mappings (polymorphisms) and Markovian operators. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 26-61. http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a1/