 The first part of the Likelihood Ratio Convergence Theorem applies to that part of the total stream of evidence (i.e., that subsequence of the total evidence stream) on which hypothesis \(h_j\) fails to be fully outcome-compatible with hypothesis \(h_i\); the second part of the theorem applies to the remaining part of the total stream of evidence, that subsequence of the total evidence stream on which \(h_j\) is fully outcome-compatible with \(h_i\). It turns out that these two kinds of cases must be treated differently. (This is due to the way in which the expected information content for empirically distinguishing between the two hypotheses will be measured for experiments and observations that are fully outcome compatible; this measure of information content blows up (becomes infinite) for experiments and observations that fail to be fully outcome compatible). Thus, the following part of the convergence theorem applies to just that part of the total stream of evidence that consists of experiments and observations that fail to be fully outcome compatible for the pair of hypotheses involved. Here, then, is the first part of the convergence theorem.