On Lin’s Condition for Products of Random Variables

Abstract

The paper presents an elaboration of some results on Lin’s conditions. A new proof is given to the fact that if densities of independent random variables ξ 1 and ξ 2 satisfy Lin’s condition, then the same is true for their product. Also, it is shown that without the condition of independence, the statement is no longer valid. © Alexander Il’inskii and Sofiya Ostrovska, 2019.