  The following result is proved:
  {\bf Theorem.} Let $D\subset \R^3$ be a bounded domain homeomorphic to a
ball, $|D|$ be its volume, $|S|$ be the surface area of its smooth boundary
$S$, $D\subset B_R:=\{x:|x|\leq R\}$, and $H_R$ is the set of all harmonic in
$B_R$ functions. If $$\frac 1 {|D|}\int_Dhdx=\frac 1 {|S|}\int_Shds\quad
\forall h\in H_R,$$ then $D$ is a ball.
