I was confronted with the following problem:
I look at probability densities on $[0,1]$ which are Lipschitz and have a Lipschitz constant smaller than some fixed $L$. Now I would like to show that this set (lets call it $U_L$) is pre-compact in $\mathcal{L}_1$.
I'm not a master of functional analysis, so any idea how to possibly handle this would help me.
Thanks a lot,
DaFischaaa