  Let $m(n,r)$ denote the minimal number of edges in an $n$-uniform hypergraph
which is not $r$-colorable. It is known that for a fixed $n$ one has \[ c_n r^n
< m(n,r) < C_n r^n. \] We prove that for any fixed $n$ the sequence $a_r :=
m(n,r)/r^n$ has a limit, which was conjectured by Alon. We also prove the list
colorings analogue of this statement.
