proof of mean square convergence of the sample mean of a stationary processnvar(X¯n)=1n∑i=1n∑j=1ncov(Xi,Xj)=∑|h|<n(1-|h|n)γ(h)≤∑|h|<n|γ(h)|If γ(n)→0 as n→∞ then limn→∞1n∑|h|<n|γ(h)|=2limn→∞|γ(n)|=0, whencevar[X¯n]→0.If ∑h=-∞∞|γ(h)|<∞ then the dominated Convergence theorem giveslimn→∞∑|h|<n(1-|h|n)γ(h)=∑h=-∞∞γ(h).