Subclasses of the weakly random reals (Q609759)

The measure-theoretical approach to define randomness for infinite binary sequences (also called reals) is via sets of measure zero (null sets): a real is random if it is not contained in any null set. If we impose effectiveness requirements on the way measure zero is defined, we obtain different effective versions of effectiveness, of which, perhaps, Martin Löf randomness is the most consecrated. This paper focuses on types of randomness weaker than Martin-Löf randomness. One category of results investigates to what extent such reals can be computed from different types of generic sets. Another category of results studies to what extent such weakly random reals can be computed from hyperimmune sets.