Geodesic
Mathematical expectations of functions of sums of a random number of independent terms
Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 387-394 Cet article a éte moissonné depuis la source Math-Net.Ru

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Conditions are found which must be imposed on a function $g(x)$, in order that $Mg(\xi_1+\xi_2+\dots+\xi_\nu)<\infty$, if $Mg(\xi_i)<\infty$ and $Mg(\nu)<\infty$, $\nu,\xi_1,\xi_2,\dots,\xi_n,\dots$ being non-negative and independent, $\nu$ being integral, and $\{\xi_i\}$ being identically distributed. The result is applied to the theory of branching processes. 
@article{MZM_1968_3_4_a2,
     author = {B. A. Sevast'yanov},
     title = {Mathematical expectations of functions of sums of a~random number of independent terms},
     journal = {Matemati\v{c}eskie zametki},
     pages = {387--394},
     year = {1968},
     volume = {3},
     number = {4},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a2/}
}
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B. A. Sevast'yanov. Mathematical expectations of functions of sums of a random number of independent terms. Matematičeskie zametki, Tome 3 (1968) no. 4, pp. 387-394. http://geodesic.mathdoc.fr/item/MZM_1968_3_4_a2/