Let Xi be a sequence of identically-distributed random variables with finite-range dependence (i.e. there exists I such that if |i-i'| ≥ I, then Xi and Xi' are independent), and a finite moment-generating function (i.e. EerXi < ∞ for all r ∈ R).
It's not too hard to show that Xi satisfies a strong law of large numbers, and I've got a proof written. However, I'm sure that this is a standard theorem in the probability literature, and I'd rather just cite it in the paper I'm writing. Do you have a good reference for this result?
Here are two follow-up generalizations: what if Xi instead has only a finite moment condition? Or what if Xi has exponential correlation decay (i.e. EXiXi' ≤ Ce-c|i-i'| for some positive c, C)?