Geodesic
On almost everywhere convergence of the Riesz averages of homogeneous random fields
Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 461-472

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Weighted averages are studied for wide-sense homogeneous random fields in $\mathbb R^k$ with spherically symmetric weights. A representation obtained for these averages permits us to prove along with a criterion for almost everywhere summability of homogeneous random fields a number of corollaries as well.
Keywords: wide-sense homogeneous random fields, spectral measure of a field, weighted averages, correlation function, almost everywhere summability, logarithmic Riesz averages. 
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     author = {V. F. Gaposhkin},
     title = {On almost everywhere convergence of the {Riesz} averages of homogeneous random fields},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {461--472},
     publisher = {mathdoc},
     volume = {42},
     number = {3},
     year = {1997},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a1/}
}
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V. F. Gaposhkin. On almost everywhere convergence of the Riesz averages of homogeneous random fields. Teoriâ veroâtnostej i ee primeneniâ, Tome 42 (1997) no. 3, pp. 461-472. http://geodesic.mathdoc.fr/item/TVP_1997_42_3_a1/