型和Keisler测度的序列逼近
Sequential approximations for types and Keisler measures
摘要：
本文是作者博士论文的修改章节。论文我们引入了序列逼近类型和序列逼近Keisler测度的概念。正如名称所暗示的那样，这些类型可以通过一系列实现的类型来近似，而度量可以通过一系列实现类型元组上的“平均度量”来近似。我们表明，一般稳定的类型（在任意的理论）和Keisler措施，这是可满足的可数模型（在NIP理论）的顺序近似。我们还介绍了一个光滑序列的概念，在一个模型上的措施，并通过这个定义给出了一般稳定的措施（在NIP理论）的等价刻画。在最后一节中，我们借此机会推广了文[8]的主要结果.
英文摘要：
This paper is a modified chapter of the author's Ph.D. thesis. We introduce the notions of sequentially approximated types and sequentially approximated Keisler measures. As the names imply, these are types which can be approximated by a sequence of realized types and measures which can be approximated by a sequence of `averaging measures' on tuples of realized types. We show that both generically stable types (in arbitrary theories) and Keisler measures which are finitely satisfiable over a countable model (in NIP theories) are sequentially approximated. We also introduce the notion of a smooth sequence in a measure over a model and give an equivalent characterization of generically stable measures (in NIP theories) via this definition. In the last section, we take the opportunity to generalize the main result of [8].
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。
