Abstract
This article concerns the dimension theory of the graphs of a family of functions which include the well-known ‘popcorn function’ and its pyramid-like higher-dimensional analogues. We calculate the box and Assouad dimensions of these graphs, as well as the intermediate dimensions, which are a family of dimensions interpolating between Hausdorff and box dimensions. As tools in the proofs, we use the Chung—Erdős inequality from probability theory, higher-dimensional Duffin—Schaeffer type estimates from Diophantine approximation, and a bound for Euler's totient function. As applications we obtain bounds on the box dimension of fractional Brownian images of the graphs, and on the Hölder distortion between different graphs.
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