  We introduce the notion of a relative limit simplicial partial motivic site
and a corresponding notion of motivic measurability which specializes to the
notion of finite schemic motivic measures of H. Schoutens and the notion of
infinite schemic motivic measures of the author. The advantage to working with
simplicial motivic sites is that it gives the correct notion of the motivic
measure of a derived stacks which have some reasonable finiteness conditions.
This work was partially supported by the Chateaubriand Fellowship.
