Geodesic
Invariant means and conditional expectation operators
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part VIII, Tome 73 (1977), pp. 207-210
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We investigate the possibility of an integral representation of conditional expectation operators. We give conditions for an integral representation of conditional expectation operators with respect to the $\sigma$-algebra of $G$-invariant sets, where $G$ is an amenable group of automorphisms of a probability space, corresponding to some partition of the space by trajectories. 
@article{ZNSL_1977_73_a15,
     author = {V. G. Kulakova},
     title = {Invariant means and conditional expectation operators},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {207--210},
     year = {1977},
     volume = {73},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_73_a15/}
}
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V. G. Kulakova. Invariant means and conditional expectation operators. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part VIII, Tome 73 (1977), pp. 207-210. http://geodesic.mathdoc.fr/item/ZNSL_1977_73_a15/