Effective support size
  Notion of effective size of support (Ess) of a random variable is introduced. A small set of natural requirements that a measure of Ess should satisfy is presented. The measure with prescribed properties is in a direct (exp-) relationship to the family of Renyi's $\alpha$-entropies. Question of selecting the value of $\alpha$ most appropriate for the purpose of measuring Ess is briefly addressed. 
M. Grendar