Relation between the irreducible representations of Lie algebras and the irreducible representations of $p$-groups

A proof is given of a theorem stating that there is a correspondence between the irreducible complex representations of a finite $p$-group and the irreducible representations of its associated nilpotent Lie algebra over a field of characteristic $p$. As a corollary it is found that the sets of degrees of the irreducible representations are the same.