We are given a sequence of independent random variables $\lbrace X_{nk} \rbrace$, for $k=1,...,r_{n}$, with $E(X_{nk})=0$ and $\sigma^{2}_{nk}<\infty$.
My question involves a small piece of the proof the CLT for Triangle Arrays with Lindeberg Condition: For an arbitrary $\epsilon >0$ and $t \in \mathbb{R}$ we consider:
$\int_{\Omega} \min\lbrace |tX_{nk}|^{2}, |tX_{nk}|^{3} \rbrace dP$
$=\int_{\lbrace |X_{nk}|>\epsilon \rbrace} \min\lbrace |tX_{nk}|^{2}, |tX_{nk}|^{3}dP + \int_{\lbrace |X_{nk}|\le \epsilon \rbrace} \min\lbrace |tX_{nk}|^{2}, |tX_{nk}|^{3}dP$
$\le \int_{\lbrace |X_{nk}|>\epsilon \rbrace}|tX_{nk}|^{2}dP + \int_{\lbrace |X_{nk}|\le \epsilon \rbrace} |tX_{nk}|^{3}dP$.
I don't understand the inequality in the last line. Can someone explain the jump from the second line to the third? Thanks in advance.