An Information-Theoretic Proof of the Central Limit Theorem with Lindeberg Conditions

The proof is based on the “information functional” $-(\int_{-\infty}^{+\infty}{p(x)\ln p(x)\,dx}+\frac12\ln\mathbf D(x))$, $p(x)$ being the density of the random variable $X$. Some new dependencies between the Shannon and Fisher information quantities are established and an information theoretic interpretation of the Lindeberg condition is given.