  Let $G$ be an $r$-uniform hypergraph on $n$ vertices such that all but at
most $\varepsilon \binom{n}{\ell}$ $\ell$-subsets of vertices have degree at
least $p \binom{n-\ell}{r-\ell}$.
  We show that $G$ contains a large subgraph with high minimum $\ell$-degree.
