  We investigate the extent to which ultrapowers by normal measures on $\kappa$
can be correct about powersets $\mathcal{P}(\lambda)$ for $\lambda>\kappa$. We
consider two versions of this questions, the capturing property
$\mathrm{CP}(\kappa,\lambda)$ and the local capturing property
$\mathrm{LCP}(\kappa,\lambda)$. $\mathrm{CP}(\kappa,\lambda)$ holds if there is
an ultrapower by a normal measure on $\kappa$ which correctly computes
$\mathcal{P}(\lambda)$. $\mathrm{LCP}(\kappa,\lambda)$ is a weakening of
$\mathrm{CP}(\kappa,\lambda)$ which holds if every subset of $\lambda$ is
contained in some ultrapower by a normal measure on $\kappa$. After examining
the basic properties of these two notions, we identify the exact consistency
strength of $\mathrm{LCP}(\kappa,\kappa^+)$. Building on results of Cummings,
who determined the exact consistency strength of
$\mathrm{CP}(\kappa,\kappa^+)$, and using a forcing due to Apter and Shelah, we
show that $\mathrm{CP}(\kappa,\lambda)$ can hold at the least measurable
cardinal.
