Hausdorff's forgotten proof that almost all numbers are normal
arXiv:2102.00493 · doi:10.1007/s00591-021-00303-w
Abstract
In 1914, Felix Hausdorff published an elegant proof that almost all numbers are simply normal in base 2. We generalize this proof to show that almost all numbers are normal. The result is arguably the most elementary proof for this theorem so far and should be accessible to undergraduates in their first year.
10 pages; fixed three small errors and an incorrect argument