Some properties of subexponential distributions

The nonnegative random variable $X$ is said to have a subexponential distribution if we have $\bigl(1-G(t)\bigr)\big/\bigl(1-F(t)\bigr)\to2$ as $t\to\infty$, where $F(t)=\mathsf P\{X\le t\}$ and $G(t)$ is the convolution of $F(t)$ with itself. Conditions on the distribution of independent nonnegative random variables $X$ and $Y$ such that $\max(X,Y)$ and $\min(X,Y)$ have a subexponential distribution are given.