In this book we shall deal with measures of information (the most important ones being called entropies), their properties, and, reciprocally, with
questions concerning which of these properties determine known measures
of information, and which are the most general formulas satisfying reasonable
requirements on practical measures of information. To the best of our
knowledge, this is the first book investigating this subject in depth. While
applications, for instance in logical games and in coding theory, will be mentioned
occasionally, we aim at giving sound foundations for these applications, for
which there are several books available. We try to avoid, however, dealing
with information measures that seem to have been introduced just for their
own sakes, with no real applications and without really useful properties
which would give hope for such applications in the future. (Of course, our
judgments may occasionally prove to be inaccurate on both counts.)