学术动态

#Math101^†Session 5

Time：Oct. 13, 2021, 13:30--15:30

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Mr. Liu, Yiheng (Class of 2024)

Title：Comparison of different types of convergence

Abstract：In this talk, we are concerned with various notions of convergence of a sequence of functions on a finite closed interval.It is obvious that uniform convergence implies both pointwise and mean convergence; however, the converse need not be true.We will clarify their relations with simple examples and introduce the concept of equicontinuity. We show that for an equicontinuous sequence, these three types of convergence are equivalent. Discussions of other types, sayconvergence in measureorconvergence in distribution, will be postponed until after the completion of a real analysis or probability course. Snacks and drinks will be provided.^††

† Seminars on analysis and algebra. Contact shuangshen@nwpu.edu.cn for any inquiry. For a history of this seminar, please visit https://teacher.nwpu.edu.cn/2017010194.

†† The refreshments are sponsored by a math competition mentors project, which is led by Prof. Ma, Rong. The support is gratefully acknowledged.