Suppose that $|X_{nk}| \leq M_n$ with probability $1$ and $M_n/s_n \rightarrow 0$. Verify Lyapounov's condition and then Lindeberg's condition.
I am little confused with the meaning of $|X_{nk}| \leq M_n$ with probability $1$? Is it mean $P(|X_{nk}| \leq M_n)=1$ or it related with the convergence with probability $1$?
What is meant is $P(|X_{nk}| \leq M_n)=1$, that is, for each row, the random variables are bounded by a bound $M_n$ which may depend on the number of the row.