Haar integral
= Haar integral
{c}
{title2=$\int_G f(g)\,d\mu(g)$}
A Haar integral integrates a function against <Haar measure>. On a compact <group>, normalizing the measure to total mass one makes it an averaging operation. Translation invariance then implies that the average of a nontrivial continuous unitary character is zero: translating the integral multiplies it by a character value different from one.