  In this paper we consider Levin's notion of mutual information in infinite
0-1-sequences, as defined in [Leonid Levin. Laws of Information Conservation
(Nongrowth) and Aspects of the Foundation of Probability Theory. Problems of
information transmission, vol. 10 (1974), pp. 206--211]. The respective
information conservation inequalities were stated in that paper without proofs.
Later some proofs appeared in the literature, however no proof of the
probabilistic conservation inequality has been published yet. In this paper we
prove that inequality and for the sake of completeness we present also short
proofs of other properties of the said notion.
