Geodesic
Integration with respect to the Euler characteristic and its applications
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 65 (2010) no. 3, pp. 399-432

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The notion of integration with respect to the Euler characteristic and its generalizations are discussed: integration over the infinite-dimensional spaces of arcs and functions, motivic integration. The author describes applications of these notions to the computation of monodromy zeta functions, Poincaré series of multi-index filtrations, generating series of classes of certain moduli spaces, and so on. Bibliography: 70 titles.
Keywords: Euler characteristic, motivic integration. 
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     author = {S. M. Gusein-Zade},
     title = {Integration with respect to the {Euler} characteristic and its applications},
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S. M. Gusein-Zade. Integration with respect to the Euler characteristic and its applications. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Tome 65 (2010) no. 3, pp. 399-432. http://geodesic.mathdoc.fr/item/RM_2010_65_3_a1/