On a conjecture of Dobrinen and Simpson concerning almost everywhere   domination
  The notions of almost everywhere (a.e.) domination and its uniform version were introduced and studied in reverse mathematics. This paper studies these notions from a recursion-theoretic point of view and explore their connections to notions such as randomness and genericity. It is shown that if $Z$ is a.e. dominating then each $1$-$Z$-random is $2$-random. In other words, $0'\leq_{\rm LR} Z$ for every a.e. dominating $Z$, where ${\rm LR}$ denotes low-for-random reducibility. Other results and corollaries are also given. 
Stephen Binns, Bj{\o}rn Kjos-Hanssen, Manuel Lerman, and Reed Solomon
math.LO