Before revision:  For a given set of sets P_1,\ldots,P_L, a composable coreset independently computes subsets C_1\subset P_1, \ldots, C_L\subset P_L, such that i=1^L C_i contains an approximation of a measure of the set i=1^L P_i.
After revision:  For a given set of sets P_1,\ldots,P_L, a composable coreset independently computes subsets C_1\subset P_1, \ldots, C_L\subset P_L, such that i=1^L C_i contains an approximation of a measure of the set i=1^L P_i.