Geodesic
Global limit theorems
Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 84-101

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Limit theorems are proved by using certain pseudometrics as distances between distributions in the scheme of summation of series of independent random variables with values in a separable Hilbert space. 
@article{ZNSL_1976_61_a8,
     author = {V. M. Kruglov},
     title = {Global limit theorems},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {84--101},
     publisher = {mathdoc},
     volume = {61},
     year = {1976},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a8/}
}
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V. M. Kruglov. Global limit theorems. Zapiski Nauchnykh Seminarov POMI, Continuity and stability in the problems of probability theory and mathematical statistics, Tome 61 (1976), pp. 84-101. http://geodesic.mathdoc.fr/item/ZNSL_1976_61_a8/