AI 中文总结
研究二元实值函数的定量稳定正则性，通过“解析对称引理”等工具证明相关引理，并对随机抽样方法进行函数理论处理，扩展了Malliaris和Shelah关于稳定图的工作。
AI 中文摘要
我们证明了二元实值函数的定量稳定正则性引理，扩展了Malliaris和Shelah关于稳定图的工作。我们的结果陈述以Chavarria、Conant和Pillay关于稳定函数的非定量定理为模型。我们定量证明中的一个关键工具是“解析对称引理”，它给出了图中一对好集的密度接近0或1这一事实的函数理论类似物。我们还对Malliaris和Shelah的随机抽样方法进行了函数理论处理，用于将由好集组成的划分细化为等分。
英文摘要
We prove quantitative stable regularity lemmas for binary real-valued functions, extending the work of Malliaris and Shelah for stable graphs. The statements of our results are modeled after non-quantitative theorems for stable functions due to Chavarria, Conant, and Pillay. One of the key tools in our quantitative proof is an "analytic symmetry lemma", which gives a function-theoretic analogue of the fact that a pair of good sets in a graph has density close to 0 or 1. We also develop a function-theoretic treatment of Malliaris and Shelah's random sampling method for refining partitions consisting of good sets into equipartitions.
Comments31 pages
