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  "body": "\n## Summary\n\nLindeberg's condition is a condition on a sequence of independent random variables with finite variances.\nIt says that no single variable contributes a non-negligible part of the total variance through its large values.\nUnder this condition, the normalised sums satisfy the [[central limit theorem|0EPZC4Z1FC]], even when the variables do not have the same distribution.\nIt is close to necessary: by a theorem of Feller, it is necessary when each variance is a negligible part of the total.\n\n## Explanations\n\n### L1 human\n\nThe central limit theorem says that a sum of many small independent effects looks normal.\nFor this, no single effect may dominate the sum.\nLindeberg's condition makes \"no effect dominates\" precise: the extreme values of each variable, taken together, carry almost none of the total variance.\nFor example, a sum of independent coin flips with different biases satisfies it as long as the total variance grows without bound.\n",
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