The weak version of the law of large numbers clarification

Question

Given a series of random variables $\{X_i\}$, where $1\leq i<n$, sharing the same expectation, but different variances and not necessarily distributed the same. Is there a rule I can apply to prove the series obeys the weak version of the law of large numbers ?

Answer 1

Basically, even the Strong Law does not require equal variances (however, it makes to proofs much more easier). For example, see the Kolmogorov's Strong Law (the weak law follows from the strong law).