Convergence multipliers

for a series of functions

Numbers , such that the series converges almost-everywhere on a measurable set , where the are numerical functions defined on .

For example, for the trigonometric Fourier series of a function from , the numbers , are convergence multipliers ( and can be chosen arbitrarily), i.e. if and if

is its trigonometric Fourier series, then the series

converges almost-everywhere on the whole real line. If , , then its trigonometric Fourier series itself converges almost-everywhere (see Carleson theorem).