  We prove existence of solutions for a class of singular elliptic problems
with a general measure as source term whose model is
  $$\begin{cases} -\Delta u = \frac{f(x)}{u^{\gamma}} +\mu & \text{in}\ \Omega,
u=0 &\text{on}\ \partial\Omega, u>0 &\text{on}\ \Omega, \end{cases} $$ where
$\Omega$ is an open bounded subset of $\mathbb{R}^N$. Here $\gamma > 0$, $f$ is
a nonnegative function on $\Omega$, and $\mu$ is a nonnegative bounded Radon
measure on $\Omega$.
