Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo

The ``analyst's traveling salesman theorem'' of geometric

measure theory characterizes those subsets of Euclidean

space that are contained in curves of finite length.

This result, proven for the plane by Jones (1990) and

extended to higher-dimensional Euclidean spaces by

Okikiolu (1991), says that a bounded set $K$ is contained

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