In mathematics, Oka's lemma, proved by Kiyoshi Oka, states that in a domain of holomorphy in
This property shows that the domain is pseudoconvex.
Historically, this lemma was first shown in the Hartogs domain in the case of two variables.
Furthermore, Oka's lemma is the inverse of Levi's problem (unramified Riemann domain over
Perhaps, this is why Oka referred to Levi's problem as "problème inverse de Hartogs", and could explain why Levi's problem is occasionally referred to as Hartogs' Inverse Problem.