Convergence of Sequences I

Abstract

In this chapter, we shall examine issues that relate to the manner in which sequences of random variables approach a limit. When we deal with sequences or series of real numbers, such issues are rather simple in their resolution, i.e., the sequence either has a unique limit or it may have several limit points; and a series may either converge to a finite number or diverge (to ±∞) or it may have no limit point, as, for example, the series $$ \sum\limits_{{i = 1}}^{\infty } {{{{\left( { - 1} \right)}}^{i}}} $$ .