摘要
本文利用函数的水平集给出函数的一些基本性质的刻画,包括函数凸性、连续性、可测性、可积性以及一些重要的应用。我们发现,在一定意义下,函数的性质完全由其水平集决定,而且方法上较为统一和直观。
In this paper, we give some properties of functions by level sets of functions, including convexity, continuity, measurable, integrability and some important applications. We find that the properties of a function are completely determined by its level set, and the methods are uniform and intuitive.
出处
《应用数学进展》
2021年第7期2278-2284,共7页
Advances in Applied Mathematics
