Abstract
We begin with a brief treatment of Hausdorff measure and Hausdorff dimension.
We then explain some of the principal results in Diophantine approximation and
the Hausdorff dimension of related sets, originating in the pioneering work of
Vojtech Jarnik. We conclude with some applications of these results to the
metrical structure of exceptional sets associated with some famous problems. It
is not intended that all the recent developments be covered but they can be
found in the references cited.
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