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MR1883931 (2003a:60049) 60F15 (60B11 60B12 60G50)
Koval, Valery A new law of the iterated logarithm in $R\sp d$ with application to matrix-normalized sums of random vectors. J. Theoret. Probab. 15 (2002), no. 1, 249--257.
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