On Khinchin’s theorem about the special role of the Gaussian distribution - Khachatryan, L. A. (Հայաստանի ԳԱԱ)
The purpose of this note is to recall one remarkable theorem of Khinchin about the special role of the Gaussian distribution. This theorem allows us to give a new interpretation of the Lindeberg condition: it guarantees the uniform integrability of the squares of normed sums of random variables and, thus, the passage to the limit under the expectation sign. The latter provides a simple proof of the central limit theorem for independent random variables.
Keywords: Mathematics