Abstract

Abstract Non-normal numbers. Exceptional sets in uniform distribution. The Besicovitch-Jarnik theorem. Generalizations with applications to the Duffin-Schaeffer problem and a two-variable problem. An exceptional set from Chapter 8. Until now we have concerned ourselves only with what is true for almost all numbers. We have not investigated the size of the exceptional sets, except to give one or two examples. The natural measure of size of an exceptional set is its Hausdorff dimension.

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