Time:  12:00  13:20 
Room: 
Doherty Hall 4303

Speaker: 
Jason Rute CMU 
Title: 
Randomness II

Abstract: 
In the previous talk of this series, Ed Dean gave a brief overview of computability theory, defined MartinLof randomness, and proved that there is a universal MartinLof test for randomness. This last result specifically shows that almost every sequence is MartinLof random. This motivates the following question: What theorems of measure theory and probability that contain the words "almost everywhere" or "almost surely" can be replaced with the stronger clause "for all MartinLof randoms"? A simple but informative example is the Strong Law of Large Numbers, which states that for almost every sequence of zeros and ones (in the faircoin probability measure) the limit of the average of the digits is 1/2. In this talk I will prove this result for MartinLof random sequences, as well as prove a few other theorems about MartinLof randomness. This is the the second in a series of talks by Ed Dean and Jason Rute. 