论文标题
动机vitushkin不变
Motivic Vitushkin invariants
论文作者
论文摘要
我们证明了涉及度量熵的真实不平等现象的非架构对应物，并测量了几何不变的$ v_i $，称为Vitushkin的变化。我们的不平等基于一组可构造动机功能的新的方便部分预订，扩展了R. Cluckers和F. loeser在可构造的动机功能和动机整合中考虑的一组。 Math。，173（2008）。我们介绍了动机整合理论和riso-triviality的概念，votushkin变化的非建筑替代品$ v_i $，尤其是数量$ v_0 $ v_0 $ v_0 $ v_0 $ connected组件。我们还证明了非Archimedean Global Cauchy-Crofton公式用于定义的尺寸$ D $，将$ v_d $和动机量度与维度$ d $相关。
We prove the nonarchimedean counterpart of a real inequality involving the metric entropy and measure geometric invariants $V_i$, called Vitushkin's variations. Our inequality is based on a new convenient partial preorder on the set of constructible motivic functions, extending the one considered by R. Cluckers and F. Loeser in Constructible motivic functions and motivic integration, Invent. Math., 173 (2008). We introduce, using motivic integration theory and the notion of riso-triviality, nonarchimedean substitutes of the Vitushkin variations $V_i$, and in particular of the number $V_0$ of connected components. We also prove the nonarchimedean global Cauchy-Crofton formula for definable sets of dimension $d$, relating $V_d$ and the motivic measure in dimension $d$.
