Distribution functions of ratio sequences. An expository paper

This expository paper presents known results on distribution functions g(x) of the sequence of blocks where x_n is an increasing sequence of positive integers. Also presents results of the set G(X_n) of all distribution functions g(x). Specially:

- continuity of g(x);

- connectivity of G(Xn);

- singleton of G(Xn);

- one-step g(x);

- uniform distribution of Xn, n = 1, 2, . . . ;

- lower and upper bounds of g(x);

- applications to bounds of ;

- many examples, e.g., , where p_n is the nth prime, is uniformly distributed.

The present results have been published by 25 papers of several authors between 2001-2013.