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^{rXi} < ∞ 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_{i}X_{i'} ≤ Ce^{-c|i-i'|} for some positive c, C)?