局部分段仿射函数及其序结构
Locally piecewise affine functions and their order structure
摘要：
在\cite{Ovchinnikov:02,Aliprantis:06a,Aliprantis:07a,Aliprantis:07}中研究了$\mathbb R^m$子集上的分段仿射函数。本文研究了局部分段仿射函数的一个更一般的概念。我们的特点是局部分段仿射函数的组件和区域。证明了正函数是局部分段仿射的当且仅当它是局部有限序列的上确界。证明了局部分段仿射函数在$C(\mathbb R^m)$中是一致稠密的，而分段仿射函数在$C(\mathbb R^m)$中是序稠密的.本文部分基于\cite{Adeeb:14}。
英文摘要：
Piecewise affine functions on subsets of $\mathbb R^m$ were studied in \cite{Ovchinnikov:02,Aliprantis:06a,Aliprantis:07a,Aliprantis:07}. In this paper we study a more general concept of a locally piecewise affine function. We characterize locally piecewise affine functions in terms of components and regions. We prove that a positive function is locally piecewise affine iff it is the supremum of a locally finite sequence of piecewise affine functions. We prove that locally piecewise affine functions are uniformly dense in $C(\mathbb R^m)$, while piecewise affine functions are sequentially order dense in $C(\mathbb R^m)$. This paper is partially based on \cite{Adeeb:14}.
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。
