Lauricella's theorem
In the theory of orthogonal functions, Lauricella's theorem provides a condition for checking the closure of a set of orthogonal functions, namely:
Theorem. A necessary and sufficient condition that a normal orthogonal set be closed is that the formal series for each function of a known closed normal orthogonal set in terms of converge in the mean to that function.
The theorem was proved by Giuseppe Lauricella in 1912.
