Partial randomness and dimension of recursively enumerable reals. (arXiv:0906.2812v1 [cs.CC])
A real \alpha is called recursively enumerable ("r.e." for short) if there
exists a computable, increasing sequence of rationals which converges to
\alpha. It is known that the randomness of an r.e. real \alpha can be
characterized in various ways using each of the notions; program-size
complexity, Martin-L\"{o}f test, Chaitin \Omega number, the domination and
\Omega-likeness of \alpha, the universality... read more
