| Résume | In a joint work with Immanuel Halupczok we introduce, on one hand, a partial preorder on the set of motivic constructible functions,
extending the one originally defined by Cluckers and Loeser, and, on the other hand, a notion of number of connected components, still in the definable
nonarchimedean context. For the last one we use the existence special canonical stratifications. Those two notions meet, for instance, in a nonarchimedean
version of a real inequality involving the metric entropy and integral-geometric invariants, called Vitushkin invariants. I will try to explain how.
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