Series: Penn State Logic Seminar Date: Tuesday, September 9, 2003 Time: 2:30 - 3:45 PM Place: 113 McAllister Building Speaker: Stephen G. Simpson, Penn State, Mathematics Title: Almost Everywhere Domination Abstract: This is joint work with Natasha Dobrinen. Consider the usual "fair coin" measure on the space C of infinite sequences of 0's and 1's. Let us say that a Turing degree d is almost everywhere dominating if, for almost all X in C, every function recursive in X is eventually dominated by a function of degree d. We present some partial results on the problem of characterizing the Turing degrees which are almost everywhere dominating. We show how this problem is related to a problem in the reverse mathematics of measure theory. We also consider some related notions and problems.