Corollary 13 (Gnedenko (1943), p. 442)

 

If Fⁿ(x) converges to a frequency distribution of the type $\phi_a (x)$, then there exist constants a_n > 0 such that

$$\lim_{n\to\infty} F^n (a_n x) = \phi_a (x).$$

Proof: This conclusion was reached in the discussion leading to Eq. (62) of Theorem 13.