发表机构
Department of Industrial and Systems Engineering, University of Southern California（工业与系统工程系，南加州大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
研究局部Lipschitz函数在Lipschitz伪度量下的强大数定律，结果在拓扑或模型理论条件下成立，应用于极限和Clarke次微分收敛等，确定了一类不会出现之前负面结果中失败现象的函数。
AI 中文摘要
我们证明了在Lipschitz伪度量下局部Lipschitz函数的强大数定律。我们的结果在拓扑条件或模型理论条件下成立，后者涵盖在o-极小结构中联合可定义的函数，但大大超出了此类。应用包括极限和Clarke次微分的一致收敛以及解的有限样本识别。因此，我们确定了一大类函数，我们之前的负面结果所揭示的失败现象不会发生。
英文摘要
We prove strong laws of large numbers for random functions in the Lipschitz pseudometric. Our results hold under either a topological or a model-theoretic condition, with the latter encompassing functions jointly definable in o-minimal structures but extending substantially beyond this class. Applications include uniform convergence of limiting and Clarke subdifferentials and finite-sample identification of solutions. Consequently, we identify broad classes of functions for which the failure phenomena revealed by our previous negative results [Tian and Royset, arXiv:2511.16568, 2025] do not occur.
Comments35 pages
