Benford's Law.
Donsker developed an extension of this theorem applying it to diffusely scaled random walks. In certain cases, the divergence of this theorem from its predicted result is given by the Berry-Esseen theorem. An extension of this theorem states that multiplying a large enough number of variables will result in a log-normal distribution leading to (*) Benford's Law. This theorem is often used to justify the applicability of a sample size of greater than 30, and its proof is similar to the proof of the law of large numbers. For 10 points, name this theorem which states that the sample mean of any independent random variable will be normal if the sample is large enough.
Donsker developed an extension of this theorem applying it to diffusely scaled random walks.
central limit theorem [or CLT]