Geodesic
Measurable partitions of the circle induced by inner functions
Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 103-106 Cet article a éte moissonné depuis la source Math-Net.Ru

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A measurable partition of $\mathbb T$ is induced by an inner function iff the corresponding operator of conditional expectation commutes with the Riesz projection. 
@article{ZNSL_1986_149_a7,
     author = {A. B. Aleksandrov},
     title = {Measurable partitions of the circle induced by inner functions},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {103--106},
     year = {1986},
     volume = {149},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a7/}
}
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A. B. Aleksandrov. Measurable partitions of the circle induced by inner functions. Zapiski Nauchnykh Seminarov POMI, Investigations on linear operators and function theory. Part XV, Tome 149 (1986), pp. 103-106. http://geodesic.mathdoc.fr/item/ZNSL_1986_149_a7/