Klain定理对紧集Minkowski对称化的推广及相关问题
Generalization of Klain's Theorem to Minkowski Symmetrization of compact sets and related topics
摘要：
我们将证明一般紧集的Minkowski代数序列的一个收敛结果。特别地，我们研究了当这个过程由其元素属于有限族的子空间序列诱导时的情况，遵循Klain在[13]中标记的路径，以及[4]和[2]中的推广。我们证明了一类特殊紧集的Fiber对称化的一个类似结果。研究了这类集合的对称化的幂等性，从而简单地推广了Klartag [14]中关于通过有限个对称化近似球的结果，并推广了[9]中的近似结果
英文摘要：
We shall prove a convergence result relative to sequences of Minkowski symmetrals of general compact sets. In particular, we investigate the case when this process is induced by sequences of subspaces whose elements belong to a finite family, following the path marked by Klain in [13], and the generalizations in [4] and [2]. We prove an analogue result for Fiber symmetrization of a specific class of compact sets. The idempotency for symmetrization of this family of sets is investigated, leading to a simple generalization of a result from Klartag [14] regarding the approximation of a ball through a finite number of symmetrizations, and generalizing an approximation result in [9]
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