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Definition 3 - Weak Convergence (Gnedenko and Kolmogorov (1954), p. 33)

  Let $\{ F_n (x)\}$ be a sequence of frequency distributions and F(x) be a frequency distribution independent of n such that at every continuity point of F(x),

\begin{displaymath} \lim_{n\to \infty} F_n(x) = F(x).\end{displaymath}

Then, Fn(x) will be said to converge weakly to F(x) as $n \to \infty$. This convergence will be denoted by the notation

\begin{displaymath} F_n (x) \Rightarrow F(x), \qquad \text{as } n \to \infty.\end{displaymath}


Leon Borgman
3/10/1998