Entropy inequalities and the central limit theorem. (Q1877517)

The paper presents two versions of central limit theorems for normalized partial sums of independent real-valued random variables, not necessarily identically distributed. The variables are assumed possessing densities (with respect to Lebesgue measure) and fulfilling some standard conditions as a uniform Lindeberg condition, bounded variance condition, etc. Theorem 1 shows convergence in Fischer information implying weak convergence and Theorem 2 shows convergence in Kullback-Leibler distance inducing \(L_1\)-convergence.