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)?

Let $X_i$ be a sequence of identically-distributed random variables with finite-range dependence (i.e. there exists $I$ such that if $|i-i'| \ge I$, then $X_i$ and $X_{i'}$ are independent), and a finite moment-generating function (i.e. $E\exp(rX_i) < \infty$ for all $r \in \mathbb{R}$).

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. $EX_iX_{i'}\le C\exp(-c|i-i'|)$ for some positive $c$, $C$)?