中文摘要：

一元粗糙函数及其数学分析性质具有意义,但当前研究主要局限于有限度量.基于无限度量研究一元粗糙函数及其数学分析性质.将度量从有限集扩展到无限集,讨论粗糙函数分类;基于无限度量研究粗糙函数的粗糙连续、粗糙极限、粗糙导数.采用无限度量,推进了一元粗糙函数及其分析性质.

英文摘要：

Univariate rough functions and their properties of mathematical analysis are meaningful, but the current research mainly confines to limited measurements. The infinite measures are adopted to research univariate rough functions and their mathematical analysis properties. First, measurements are expanded from a finite set to an infinite set, and the rough function classification is discussed. Based on infinite measures, rough continuity,limit, derivative of rough functions are investigated. This study utilizes infinite measures to promote univariate rough functions and their analysis properties.