 Pompeiu problem

In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929, 
as follows.Suppose "f" is a nonzero continuous function defined on a Euclidean space, and "K" is a simply connected Lipschitz domain, so that the integral of "f" vanishes on every congruent copy of "K".Then the domain is a ball.