A general strong law of large numbers for additive arithmetic functions
نویسنده
چکیده
Let f(n) be a strongly additive complex valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑ N n=1 f(n)Xn ∑ N n=1 f(n) a.s. = EX.
منابع مشابه
On the strong law of large numbers and additive functions
Let f(n) be a strongly additive complex-valued arithmetic function. Under mild conditions on f , we prove the following weighted strong law of large numbers: if X, X1, X2, . . . is any sequence of integrable i.i.d. random variables, then lim N→∞ ∑N n=1 f(n)Xn ∑N n=1 f(n) = EX a.s.
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