Uncorrelatedness sets of bounded random variables

An uncorrelatedness set of two random variables shows which powers of random variables are uncorrelated. These sets provide a measure of independence: the wider an uncorrelatedness set is, the more independent random variables are. Conditions for a subset of N2 to be an uncorrelatedness set of bounded random variables are studied. Applications to the theory of copulas are given.  2004 Elsevier Inc. All rights reserved