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 { u k } {\displaystyle \{u_{k}\}} be closed is that the formal series for each function of a known closed normal orthogonal set { v k } {\displaystyle \{v_{k}\}} in terms of { u k } {\displaystyle \{u_{k}\}} converge in the mean to that function. The theorem was proved by Giuseppe Lauricella in 1912.