您好，我想问的问题如下:
已知lg(n!) = Θ(n*lg n)
1. (lg n)! is not Polynomailly Bounded
lg(lg n)! = Θ(lg n * lg (lg n))
= Θ(lg n * lglg n)
= ω(lg n)
因为lg(lg n)! != O(lg n)，所以(lg n)! 不是 Polynomail-Bounded
2. (lglg n)! is Polynomailly Bounded
lg(lglg n)! = Θ(lglg n * lg (lglg n))
= O((lglg n)^2)
= O(lg^2(lg n))
= O(lg n)
因为lg(lglg n)! = o(lg n)，所以(lglg n)!是Polynomail-Bounded
Q: 关于1.中的叙述，lg(lg n)!是否可以取
log(log n)! = Θ(lg n * lglg n)
= O((lg n)^2) = O(lg^2 n)
然后就说明因为lg(f(n)) != O(lg n)，所以f(n)不是Polynomail-Bounded?
还是说得要取little-omega，找到lg(f(n)) > ω(lgn)，
才可以说明不是Polynomail-Bounded?