Abstract
We consider a sequence of independent random variables with zero expectations E zn . Further let
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‘Über das Gesetz des iterierten Logarithmus’, Math. Ann. 101 (1929), 126-135.
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Notes
See his book Basic laws of probability theory, Moscow, 1927 (in Russian).
Math. Ann.99 (1928), 152.
See: S. Bernshtein, ‘On a variation of Chebyshev’s inequality and the error of Laplace’s formula’, Uchen. Zap. Nauch.-Issl. Kafedr. Ukrain. Otd. Mat. 1 (1924), 38-48 (in Russian). (See also: Collected works, Vol. 4, pp. 71-79).
The + sign is used instead of ∪ in order to stress the fact that the events in question are pairwise incompatible.
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Shiryayev, A.N. (1992). On The Law of The Iterated Logarithm. In: Shiryayev, A.N. (eds) Selected Works of A. N. Kolmogorov. Mathematics and Its Applications (Soviet Series), vol 26. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2260-3_5
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DOI: https://doi.org/10.1007/978-94-011-2260-3_5
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