  We prove global gradient estimates for parabolic $p$-Laplace type equations
with measure data, whose model is $$u_t - \textrm{div} \left(|Du|^{p-2}
Du\right) = \mu \quad \textrm{in} \ \Omega \times (0,T) \subset \mathbb{R}^n
\times \mathbb{R},$$ where $\mu$ is a signed Radon measure with finite total
mass. We consider the singular case $$\frac{2n}{n+1} <p \le 2-\frac{1}{n+1}$$
and give possibly minimal conditions on the nonlinearity and the boundary of
$\Omega$, which guarantee the regularity results for such measure data
problems.
