  A theorem of Wiegerinck says that the Bergman space over any domain in
$\mathbb C$ is either trivial or infinite dimensional. We generalize this
theorem in the following form. Let E be a hermitian, holomorphic vector bundle
over $\mathbb P^1$, the later equipped with a volume form and $D$ an arbitrary
domain in $\mathbb P^1$. Then the space of holomorphic L2 sections of $E$ over
$D$ is either equal to $H^0(M,E)$ or it has infinite dimension.
