2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/131039Notion 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 $α$-entropies. Question of selecting the value of $α$ most appropriate for the purpose of measuring Ess is briefly addressed.Statistics Theory94A17text