Resumen de Every Random Variable Satisfies a Certain Nontrivial Integrability Condition

Alberto Lekuona Amiano, José Antonio Adell Pascual

• We show that every random variable X fulfils a certain nontrivial integrability condition, in the sense that there always exists a nonnegative function g¿depending on X¿growing to 1 as x ! 1, and such that Eg(jXj) < 1. Refinements of this universal property allow us to give some simple but striking statements in connection with Markov¿s inequality and the central limit theorem.