Lindeberg's condition

Summary

Lindeberg's condition is a condition on a sequence of independent random variables with finite variances. It says that no single variable contributes a non-negligible part of the total variance through its large values. Under this condition, the normalised sums satisfy the central limit theorem, even when the variables do not have the same distribution. It is close to necessary: by a theorem of Feller, it is necessary when each variance is a negligible part of the total.