INTEGRATION AND CELL DECOMPOSITION IN P-MINIMAL STRUCTURES

We show that the class of L-constructible functions is closed under integration for any P-minimal expansion of a p-adic field (K, L). This generalizes results previously known for semi-algebraic and subanalytic structures. As part of the proof, we obtain a weak version of cell decomposition and function preparation for P-minimal structures, a result which is independent of the existence of Skolem functions. A direct corollary is that Denef's results on the rationality of Poincare series hold in any P-minimal expansion of a p-adic field (K, L).