Let X_i be a sequence of identically-distributed random variables with finite-range dependence (i.e. there exists I such that if |i-i'| ≥ I, then X_i and X_i' are independent), and a finite moment-generating function (i.e. Ee^rX_i < ∞ for all r ∈ R).

It's not too hard to show that X_i 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 X_i instead has only a finite moment condition? Or what if X_i has exponential correlation decay (i.e. EX_iX_i' ≤ Ce^-c|i-i'| for some positive c, C)?