Measuring definable sets in o-minimal fields
Measuring definable sets in o-minimal fields
复制标题
测量最小域中的可定义集合
DOI：
10.1007/s11856-015-1234-0
复制
发表时间：
2015
期刊：
影响因子：
--
通讯作者：
J.Marikova
中科院分区：
文献类型：
--
作者：
Takuji Nakamura;Yasutaka Nakanishi;Shin Satoh b;Akira Yasuhara;J.Marikova
我们在o-极小域的笛卡尔幂的有限部分所包含的可定义集上引入了一种非实值测度。该度量取值于序半环，即商OFR的Dedekind完备化。我们证明了具有非空内部的Rn的每个可测子集都有正测度，并且该测度是由雅可比行列式等于±1的可定义的C_1-微分同胚保持的。
We introduce a non-real-valued measure on the definable sets contained in the finite part of a cartesian power of an o-minimal fieldR. The measure takes values in an ordered semiring, the Dedekind completion of a quotient ofR. We show that every measurable subset ofRnwith non-empty interior has positive measure, and that the measure is preserved by definableC1-diffeomorphisms with Jacobian determinant equal to ±1.