# Mean-periodic function

${\displaystyle \int f(x-y)\,d\mu (y)=0\qquad \qquad (1)}$
where ${\displaystyle \mu }$ is the difference between the Dirac measures at 0 and a. A mean-periodic function is a function ƒ satisfying (1) for some nonzero measure ${\displaystyle \mu }$ with compact (hence bounded) support.