  We address three outstanding problems in information theory. Problem one is
the definition of a non-negative decomposition of the information conveyed by
two or more sources about a target variable into the specific contribution of
each possible combination of the sources. Problem two is the definition of a
measure of information shared by several sources about the target variable.
Problem three is the definition of a measure of multiple mutual information,
that is, the extension of mutual information to more than two variables.
