Submission date: 21 April 2020

Abstract:

We define the operation of evaluation at a point for motivic constructible (exponential) functions from the Cluckers-Loeser framework of motivic integration and show that two such motivic functions are abstractly equal if and only if their evaluations at each point are the same. We similarly characterise relative integrability, namely, in terms of integrability in each fiber separately. These results simplify the mentioned and related frameworks of motivic integration and their usage.

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Full text arXiv 2004.09981: pdf, ps.