Almost sure convergence, uniformly integrable and L1 convergence

Question

I am learning the convergence of martingale. Then I saw a theorem from my textbook which implies a theorem in measure theory which states "Let {Xn,n ∈ N} be a sequence of random variables which converges almost surely to a random variable X. Then Xn converges in L1 to X if and only if {Xn, n ∈ N} is uniformly integrable." Is there any proof for this theorem? thanks!