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arXiv 1306.5807math.FAmath.MG
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Radon-Nikodrom性质与测地线的厚族

Radon-Nikodým property and thick families of geodesics

Mikhail I. Ostrovskii

发表信息：
J. Math Anal. Appl., 409 (2014), no. 2, 906-910
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摘要：

没有Radon-Nikodschitz性质的Banach空间被刻画为包含如下定义的厚测地线族的双利普希茨像的空间。度量空间中连接点$u$和$v$的测地线族$T$称为{ \it厚}，如果存在$α>0$，使得对于每个$g\in T$和$g$的图像中的点$r_1,...,r_n$的任何有限集合，存在另一个$uv$ -测地线$\widetilde g\in T$，满足以下条件：$\widetilde g$也穿过$r_1,...,r_n$，并且可能与$g$有一些更多的公共点。另一方面，存在$g$和$\widetilde g$的公共点的有限集合，其包含$r_1,...,r_n$，并且使得这些公共点之间的测地线的最大偏差之和至少为$α$。

英文摘要：

Banach spaces without the Radon-Nikodým property are characterized as spaces containing bilipschitz images of thick families of geodesics defined as follows. A family $T$ of geodesics joining points $u$ and $v$ in a metric space is called {\it thick} if there is $α>0$ such that for every $g\in T$ and for any finite collection of points $r_1,...,r_n$ in the image of $g$, there is another $uv$-geodesic $\widetilde g\in T$ satisfying the conditions: $\widetilde g$ also passes through $r_1,...,r_n$, and, possibly, has some more common points with $g$. On the other hand, there is a finite collection of common points of $g$ and $\widetilde g$ which contains $r_1,...,r_n$ and is such that the sum of maximal deviations of the geodesics between these common points is at least $α$.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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