Geodesic
Global limit theorems
Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 123-127

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In the paper, necessary and sufficient conditions for convergence in the mean of probability distribution functions are given. 
@article{TVP_1976_21_1_a8,
     author = {V. M. Kruglov},
     title = {Global limit theorems},
     journal = {Teori\^a vero\^atnostej i ee primeneni\^a},
     pages = {123--127},
     publisher = {mathdoc},
     volume = {21},
     number = {1},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a8/}
}
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V. M. Kruglov. Global limit theorems. Teoriâ veroâtnostej i ee primeneniâ, Tome 21 (1976) no. 1, pp. 123-127. http://geodesic.mathdoc.fr/item/TVP_1976_21_1_a8/