Rademacher–Menchov theorem

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

Statement

If the coefficients c_ν of a series of bounded orthogonal functions on an interval satisfy

$\sum |c_{\nu }{|}^2\log (\nu {)}^2<\mathrm{\infty }$

then the series converges almost everywhere.

References

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