Geodesic
A strong law of large numbers for orthogonal random variables
Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 103-106

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A generalization of one theorem of K. Tandori is proved. A sufficient condition is derived for application of a strong law of large numbers to a sequence of orthogonal random variables, expressed in terms of the growth of sums of second moments of these variables. 
@article{ZNSL_1977_72_a7,
     author = {V. V. Petrov},
     title = {A strong law of large numbers for orthogonal random variables},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {103--106},
     publisher = {mathdoc},
     volume = {72},
     year = {1977},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a7/}
}
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V. V. Petrov. A strong law of large numbers for orthogonal random variables. Zapiski Nauchnykh Seminarov POMI, Problems of the theory of probability distributions. Part IV, Tome 72 (1977), pp. 103-106. http://geodesic.mathdoc.fr/item/ZNSL_1977_72_a7/