## Feller-Lévy Condition

Given a sequence of independent random variates , , ..., if and

then

This means that if the Lindeberg Condition holds for the sequence of variates , ..., then the Variance of an individual term in the sum of is asymptotically negligible. For such sequences, the Lindeberg Condition is Necessary as well as Sufficient for the Lindeberg-Feller Central Limit Theorem to hold.

References

Zabell, S. L. Alan Turing and the Central Limit Theorem.'' Amer. Math. Monthly 102, 483-494, 1995.