Lecturer:Yan Jia'an

Abstract:This short-term course will systematically introduce the fundamentals of measure theory, integral theory and relevant probability theory. The course is aimed at senior undergraduate and graduate students majoring in mathematics and it is divided into six lectures:

Lecture 1: Monotone class theorem (set form), theorem of extension of measure.

Lecture 2: Monotone class theorem (function form), convergence of sequence of measurable functions.

Lecture 3: Integral, indefinite integral and signed measure, L^p space and its duality.

Lecture 4: Product measure, Fubini theorem, probability measure on infinite product space.

Lecture 5: Measure convergence, independence, conditional mathematical expectation and conditional independence.

Lecture 6: Uniform integrability of family of random variables, stationary sequence and ergodic theorem.

Introduction to the Lecturer:Yan Jia'an is a famous mathematician in China, academician of the Chinese Academy of Sciences (CAS) and researcher of the Academy of Mathematics and Systems Science, Chinese Academy of Sciences. He was born in Hanjiang County, Jiangsu Province in 1941 and graduated from the Department of Applied Mathematics of University of Science and Technology of China in 1964. He is mainly engaged in the research of stochastic analysis and financial mathematics, and has made outstanding achievements in the fields of probability theory, martingale theory, stochastic analysis and white noise analysis. He has published more than 80 important papers and 9 teaching material monographs. He won the first prize of CAS Natural Science Award in 1992, the National Natural Science Award (second class) in 1993, the S&T Progress Award of Ho Leung Ho Lee Foundation in 2006 and the Hua Luogeng Prize in Mathematics in 2007. He was invited to make a 45 minute report at the 24^thInternational Congress of Mathematicians.

Invitee:Chen Zengjing, Professor from School of Mathematics

Time:2021.09.22-2021.09.24, 2021.09.26-2021.09.28

14:00-17:00 p.m.

Venue:Academic Hall #924, Block B, Zhixin Building, Central Campus

Hosted by the School of Mathematics, Shandong University