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

Grauert-Riemenschneider multiplier ideal sheaves and the (optimal) Brian\c{c}on-Skoda number