学术动态

#RAFS^†Session 13

Time：Mar. 26, 2021, 10:00--12:00

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Mr. Gao, Chaoqun (Class of 2021)

Title：Examples of metric spaces

Abstract：We will investigate three examples of metric spaces: the set of real-valued continuous functions endowed withthe uniform metric, the setRof Riemann integrable functions on an interval with the usual pseudo metric, and the classSof sets of finite measuremwith the symmetric difference metric (Fréchet-Nikodym metric). We will discuss whether these spaces are complete or not, and remark that there exists an isometric embedding ofRinS, whenmis taken to bethe2-dimensional Lebesgue measure in the plane. In particular, it is possible to identify the closure ofRinSwith the space of Lebesgue integrable functions, thus providing one motivation for enlarging the class of integrable functions.

† Real Analysis Friday Seminars. Contactshuangshen@nwpu.edu.cnfor any inquiry. For a history of this seminar, please visithttps://teacher.nwpu.edu.cn/2017010194.