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 
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/
@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/}
}
TY  - JOUR
AU  - V. G. Kulakova
TI  - Invariant means and conditional expectation operators
JO  - Zapiski Nauchnykh Seminarov POMI
PY  - 1977
SP  - 207
EP  - 210
VL  - 73
UR  - http://geodesic.mathdoc.fr/item/ZNSL_1977_73_a15/
LA  - ru
ID  - ZNSL_1977_73_a15
ER  - 
%0 Journal Article
%A V. G. Kulakova
%T Invariant means and conditional expectation operators
%J Zapiski Nauchnykh Seminarov POMI
%D 1977
%P 207-210
%V 73
%U http://geodesic.mathdoc.fr/item/ZNSL_1977_73_a15/
%G ru
%F ZNSL_1977_73_a15

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

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.