Definition 6

  The concept of weak convergence introduced in Definition 3 will be modified for use with W-functions. Let w_n(x), $n = 1,2,3,\ldots$, be a sequence of monotonic functions and w(x) be a W-function such that at every continuity point of w(x) and at every value of x where $w(x) = \infty$,

$$\lim_{n\to\infty} w_n(x) = w(x).$$

Then, w_n(x) will be said to converge weakly to w(x). This convergence will be denoted symbolically as

$$w_n(x) \Rightarrow w(x).$$