$X_n = X \land n$ is square integrable

Question

If X is in $L^+(\Omega,\mathscr A, P)$ (denoting all nonnegative random variables). Why $X_n = X \land n$ is square integrable?

Answer 1

$|X\wedge n|\leq n,$ so $\int_{\Omega} |X\wedge n|^2\textrm{d}P\leq n^2P(\Omega)=n^2<\infty,$ if $P$ is a probability measure