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Grothendieck rings of definable subassignments and equivariant motivic measures

This paper studies categories of definable subassignments with some category equivalences to semialgebraic and constructible subsets of arc spaces of algebraic varieties. These equivalences lead to the identity of certain Grothendieck rings, which allows us to compare the motivic measure of Cluckers-Loeser with that of Denef-Loeser for certain classes of definable subassignments. |