Base-invariance implies Benford’s law

@inproceedings{Hill1995BaseinvarianceIB,
  title={Base-invariance implies Benford’s law},
  author={Theodore P. Hill},
  year={1995}
}
A derivation of Benford's Law or the First-Digit Phenomenon is given assuming only base-invariance of the underlying law. The only baseinvariant distributions are shown to be convex combinations of two extremal probabilities, one corresponding to point mass and the other a log-Lebesgue measure. The main tools in the proof are identification of an appropriate mantissa cr-algebra on the positive reals, and results for invariant measures on the circle. 

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