Hi all,

I'm trying to learn precompactness arguments , I have a question about precompactness in function spaces $\displaystyle L_{p} $ and C[0,1] :

Prove the set $\displaystyle A = (sin(nt) )_{n=0}^{\infty} $ is precompact in $\displaystyle L_{p}(0,1)$ for $\displaystyle 1 \leq p < \infty $ , but it's not precompact in C[0,1]. I looked at the theorems about equicontinuity and similar stuff but I couldn't find anything useful , can anyone give a hint??