Information conditions for a class of limit theorems for the sequence of m-valued random variables (Q910811)

The main purpose of this paper is to study the relation between the relative entropy density and limit theorems for the sequence \(\{X_ n\), \(n\geq 1\}\) of m-valued random variables. A theorem is proved giving sufficient conditions for a class of limit theorems for \(\{X_ n\}\). The conditions are expressed using notions of information theory, namely relative entropy density and entropy density deviation.