Théorème de Lauricella

Texte anglais à traduire :
A necessary and sufficient condition that a normal orthogonal set ${\displaystyle \{u_{k}\}}$ be closed is that the formal series for each function of a known closed normal orthogonal set ${\displaystyle \{v_{k}\}}$ in terms of ${\displaystyle \{u_{k}\}}$ converge in the mean to that function.