Geodesic
A note on measurable additive lifting in a measure space of measurable functions
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 150-153

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Some conditions for the existence of measurable additive lifting are discussed. 
@article{ZNSL_1977_72_a13,
     author = {V. N. Sudakov},
     title = {A note on measurable additive lifting in a measure space of measurable functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {150--153},
     publisher = {mathdoc},
     volume = {72},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a13/}
}
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V. N. Sudakov. A note on measurable additive lifting in a measure space of measurable functions. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 150-153. http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a13/