  Suppose we are given two probability measures on the set of one-way infinite
finite-alphabet sequences and consider the question when one of the measures
predicts the other, that is, when conditional probabilities converge (in a
certain sense) when one of the measures is chosen to generate the sequence.
This question may be considered a refinement of the problem of sequence
prediction in its most general formulation: for a given class of probability
measures, does there exist a measure which predicts all of the measures in the
class? To address this problem, we find some conditions on local absolute
continuity which are sufficient for prediction and which generalize several
different notions which are known to be sufficient for prediction. We also
formulate some open questions to outline a direction for finding the conditions
on classes of measures for which prediction is possible.
