Rademacher–Menchov theorem

In mathematical analysis, the Rademacher–Menchov theorem, introduced by and, gives a sufficient condition for a series of orthogonal functions on an interval to converge almost everywhere.

Statement
If the coefficients cν of a series of bounded orthogonal functions on an interval satisfy
 * $$\sum |c_\nu|^2\log(\nu)^2<\infty$$

then the series converges almost everywhere.