J. Gregory and . Chaitin, Nonrecursive infinite strings with simple initial segments, IBM Journal of Research and Development, vol.21, pp.350-359, 1977.

R. Downey, D. R. Hirschfeldt, J. S. Miller, and A. Nies, RELATIVIZING CHAITIN'S HALTING PROBABILITY, Journal of Mathematical Logic, vol.05, issue.02, pp.167-192, 2005.
DOI : 10.1142/S0219061305000468

G. Rodney, D. R. Downey, and . Hirschfeldt, Algorithmic randomness and complexity. Theory and Applications of Computability, 2010.

P. Gács, Every sequence is reducible to a random one, Information and Control, vol.70, issue.2-3, pp.186-192, 1986.
DOI : 10.1016/S0019-9958(86)80004-3

R. Denis, A. Hirschfeldt, F. Nies, and . Stephan, Using random sets as oracles, J. Lond. Math. Soc, issue.23, pp.75610-622, 2007.

B. Kjos-hanssen, Low for random reals and positive-measure domination, Proc. Amer, pp.3703-3709, 2007.
DOI : 10.1090/S0002-9939-07-08648-0

A. Ku?era and . Measure, Measure, ?? 1 0 -classes and complete extensions of PA, Recursion theory week (Oberwolfach, pp.245-259, 1984.
DOI : 10.1016/S0049-237X(08)71117-0

S. Joseph, L. Miller, and . Yu, On initial segment complexity and degrees of randomness, Trans. Amer. Math. Soc, vol.360, issue.6, pp.3193-3210, 2008.

A. Nies, Lowness properties and randomness, Advances in Mathematics, vol.197, issue.1, pp.274-305, 2005.
DOI : 10.1016/j.aim.2004.10.006

A. Nies, Computability and randomness, volume 51 of Oxford Logic Guides, 2009.

B. David, R. W. Posner, and . Robinson, Degrees joining to 0, J. Symbolic Logic, vol.46, issue.4, pp.714-722, 1981.

J. Reimann and T. A. Slaman, Measures and their random reals. To appear in the Transactions of the
DOI : 10.1090/s0002-9947-2015-06184-4

URL : http://arxiv.org/abs/0802.2705

G. Stephen, F. Simpson, and . Stephan, Cone avoidance and randomness preservation

R. M. Solovay, Draft of paper (or series of papers) on Chaitin's work. Unpublished notes, 215 pages, 1975.

. Michiel-van-lambalgen, Abstract, The Journal of Symbolic Logic, vol.II, issue.03, pp.1143-1167, 1990.
DOI : 10.1007/BF01111205

L. Yu, Characterizing strong randomness via Martin-L??f randomness, Annals of Pure and Applied Logic, vol.163, issue.3, pp.214-224, 2012.
DOI : 10.1016/j.apal.2011.08.006