On Lin's condition for products of random variables with singular joint distribution

摘要

Lin’s condition is used to establish the moment determinacy/indeterminacy of absolutely continuous probability distributions. Recently, a number of papers related to Lin’s condition for functions of randomvariables have appeared. In the present paper, this condition is studied forproducts of random variables with given densities in the case when theirjoint distribution is singular. It is proved, assuming that the densities of bothrandom variables satisfy Lin’s condition, that the density of their productmay or may not satisfy this condition.