Solution
= Solution
For every $\epsilon>0$, $1_{|X_n-X|>\epsilon}\to0$ almost surely and is dominated by 1, so its expectation, the corresponding probability, tends to zero.
= Solution
For every $\epsilon>0$, $1_{|X_n-X|>\epsilon}\to0$ almost surely and is dominated by 1, so its expectation, the corresponding probability, tends to zero.