Weak Laws of Large Numbers for Dependent Random Variables

In this paper we will prove several weak laws of large numbers for dependent random variables. The weak dependence concept that is used is the mixingale concept. From the weak laws of large numbers for triangular arrays of mixingale random variables, weak laws for mixing and near epoch dependent random variables follow. Features of the weak laws of large numbers that are proven here is that they impose tradeoff conditions between dependence and trending of the summands.