In this paper we consider Levin's notion of mutual information in infinite 0-1-sequences, as defined in Levin (1974) [6]. 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.

中文翻译：

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1974年Levin的共同信息概念的守恒不等式证明

在本文中，我们考虑了Levin（1974）[6]中定义的无限0-1序列中的Levin互信息概念。该文件中陈述了各自的信息保存不等式，没有证据。后来一些证据出现在文献中，但是尚未发表关于概率守恒不平等的证据。在本文中，我们证明了不等式，并且为了完整性，我们还提供了该概念其他性质的简短证明。