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Hill1995

T. Hill, "Base-invariance implies Benford's law," Proc. Amer. Math. Soc., 123:3 (March 1995) 887--895. [Hill demonstrates that scale invariance implies base invariance, and that base invariance implies Benford's law. So if we assume that a distribution must be scale invariant, i.e., changing measurement units does not change the shape of the distribution, then that distribution must satisfy Benford's law.]