I want to show that: $$ \frac{1}{n}\sum_{i=1}^n Y_{i,n}\overset{p}{\to}\lim_{n\to\infty}\frac{1}{n}\sum_{i=1}^nE(Y_{i,n}) $$ Given that $Y_{i,n}$ are independent across $i$, for any given $n$. There might be some other conditions missing, which I also have to figure out. I know Kolmogorov's SLLN.
Any tips on how to proceed?