We show that there is a low T-upper bound for the class of K-trivial sets, namely those which are weak from the point of view of algorithmic randomness. This result is a special case of a more general characterization of ideals in the T-degrees below 0 for which there is a low T-upper bound.
We show that for every K-trivial real X, there is no representation of a continuous probability measure m such that X is 1-random relative to m.
