Definably amenable NIP groups
Definably amenable NIP groups
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DOI：
10.1090/jams/896
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发表时间：
2015-02
期刊：
影响因子：
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通讯作者：
A. Chernikov;Pierre Simon
中科院分区：
文献类型：
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作者：
A. Chernikov;Pierre Simon
我们研究明确顺从的NIP群体。我们开发了一个理论的泛型，表明以前考虑的各种定义相吻合，并研究不变的措施。应用包括：正则遍历测度的特征，证明Petrykowski猜想连接存在的有界轨道与可定义的顺从性在NIP的情况下，和埃利斯群猜想的Newelski和Pillay连接的模型理论连通组件的NIP群与理想子群的埃利斯包络半群。
We study definably amenable NIP groups. We develop a theory of generics, showing that various definitions considered previously coincide, and study invariant measures. Applications include: characterization of regular ergodic measures, a proof of the conjecture of Petrykowski connecting existence of bounded orbits with definable amenability in the NIP case, and the Ellis group conjecture of Newelski and Pillay connecting the model-theoretic connected component of an NIP group with the ideal subgroup of its Ellis enveloping semigroup.