  We give solutions to two of the questions in a paper by Brendle,
Brooke-Taylor, Ng and Nies. Our examples derive from a 2014 construction by
Khan and Miller as well as new direct constructions using martingales.
  At the same time, we introduce the concept of i.o. subuniformity and relate
this concept to recursive measure theory. We prove that there are classes
closed downwards under Turing reducibility that have recursive measure zero and
that are not i.o. subuniform. This shows that there are examples of classes
that cannot be covered with methods other than probabilistic ones. It is easily
seen that every set of hyperimmune degree can cover the recursive sets. We
prove that there are both examples of hyperimmune-free degree that can and that
cannot compute such a cover.
