On Martin-Löf (non-)convergence of Solomonoff's universal mixture

We study the convergence of Solomonoff's universal mixture on individual Martin-Löf random sequences. A new result is presented extending the work of Hutter and Muchnik [3] by showing that there does not exist a universal mixture that converges on all Martin-Löf random sequences. We show that this is not an artifact of the fact that the universal mixture is not a proper measure and that the normalised universal mixture also fails to converge on all Martin-Löf random sequences.