Frolov Andrei N - Universal Theory For Strong Limit Theorems Of Probability

i.i.d. independent, identically distributed

d.f. distribution function

c.f. characteristic function

m.g.f. moment generating function

a.s. almost surely

w.p. 1 with probability 1

i.o. infinitely often

LDT large deviations theory

SLLN strong law of large numbers

LIL law of the iterated logarithm

CLT central limit theorem

end of a proof

R the set of real numbers

N the set of natural numbers

an = o(bn) means that an/bn 0

an = O(bn) means that lim sup |an|/bn <

anbn means that an/bn 1

IB(x) the indicator of a Borel set B

IB the indicator of an event B

DX the variation of a random variable X

DN() domain of normal attraction of the asymmetric stable law with exponent > 1

D() domain of non-normal attraction of the asymmetric stable law with exponent > 1

SVa the set of slowly varying at a functions

RVa the set of regularly varying at a functions

f1(x) the inverse function to f(x)

#B the number of elements of a finite set B

[x] the integer part of x

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