The proof of the theorem is a single line and thus seemingly straightforward, yet I cannot see how to justify it. I tried to rearrange some of the pieces, but that approach failed to improve my understanding. Any help in justifying the statement would be greatly appreciated.
If there is a $varphige0$ so that $varphi(x)tointfy$ as $|x|toinfty$ and
then $F_n$ is tight.