  The goal of this note is to survey some recent results on the
Grauert-Riemenschneider multiplier ideal sheaves on any (reduced) complex space
of pure dimension. In particular, we obtain the Brian\c{c}on-Skoda number for
any Noetherian ring of weakly holomorphic functions with weakly rational
singularities (\emph{not} essentially of finite type over $\mathbb{C}$ and
Cohen-Macaulay local rings), which will partially answer a question of Huneke.
