Geodesic
On an extremal problem in probability theory
Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 579-584

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The paper considers the problem of finding the absolute maximum and the absolute minimum of functional (1) where $x$ and $y$ are two dependend vector-valued random variables and $Q(y\mid x)$ is an unknown conditional distribution function. The problem is solved when $I_Q(x)$ is a monotone function of all the variables $x$ and the density functions of the random variables $x$ and $y$ are known. 
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     author = {G. D. Kartashov and A. N. Yavriyan},
     title = {On an extremal problem in probability theory},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {579--584},
     publisher = {mathdoc},
     volume = {10},
     number = {3},
     year = {1965},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a21/}
}
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G. D. Kartashov; A. N. Yavriyan. On an extremal problem in probability theory. Teoriâ veroâtnostej i ee primeneniâ, Tome 10 (1965) no. 3, pp. 579-584. http://geodesic.mathdoc.fr/item/TVP_1965_10_3_a21/