  We show how to determine the maximum and minimum possible values of one
measure of entropy for a given value of another measure of entropy. These
maximum and minimum values are obtained for two standard forms of probability
distribution (or quantum state) independent of the entropy measures, provided
the entropy measures satisfy a concavity/convexity relation. These results may
be applied to entropies for classical probability distributions, entropies of
mixed quantum states and measures of entanglement for pure states.
