In this short note, we present a new version of the Central Limit Theorem whose proof is based on Levy's characterization of Brownian motion. The method in the proof may allow to extend the result to a more general context, e.g. to averaged sums of properly compensated dependent random variables.
"A New Version of the Central Limit Theorem." Afr. Diaspora J. Math. (N.S.) 19 (1) 12 - 20, 2016.