Full paper in PDF format:
$%E. Gorsky, On the motivic measure on the space of functions, Rev. Mat. Complut. 20 (2007), no. 2, 507–521.%$

On the Motivic Measure on the Space of Functions
Evgeny GORSKY
Moscow State University
Moscow — Russia

gorsky@mccme.ru

Received: February 16, 2007
Accepted: May 3, 2007

ABSTRACT

Motivic measure on the space of functions was introduced by Campillo, Delgado, and Gusein-Zade as an analog of the motivic measure on the space of arcs. In this paper we prove that the measure on the space of functions can be related to the motivic measure on the space of arcs by a factor, which can be defined explicitly in geometric terms. This provides a possibility to rewrite motivic integrals over the space of functions as integrals over the union of all symmetric powers of the space of arcs.

Key words: motivic integration, Milnor number.
2000 Mathematics Subject Classification:
32S99, 28B10.