Random Variables Fundamental in Probability and Sigma-Complete Convergence

摘要

The aim of this paper is to study some necessary and sufficient conditions for fundamental (Cauchy) in probability sequences of random variables. In this way, we will be able to deduce some relationships between certain types of convergence and these sequences of random variables characterized because in their definition the random variable limit does not appear. Finally, we introduce the concept of a Sigma-completely convergent sequence and a sufficient condition for it.