学术动态

#Math101 Session 12

Time：Dec. 17, 2021, 16:00--18:00

Location：434 Qi Xiang Building, Chang'an Campus

Speaker：Mr.Zhang,Zhenhao (Class of 2024)

Title：Normal numbers without measure theory

Abstract：A real number is said to be simply normal to base 2 if it has a roughly equal number of zeros and ones in its binary expansion. The classic 1909 theorem by E. Borel asserts that almost every number is simply normal to base 2 (as a matter of fact, Borel showed in the seminal paper a much stronger result that almost every number is normal to all integer bases). Following M. Kac and R. Nillsen, we will prove this result with the help of Rademacher functions via a totally elementary approach.Connections to diverse areas including probability and ergodic theory will be briefly mentioned.This talk has no prerequisite for Lebesgue measure theory.