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arXiv · 2311.16210

An uncountable union of line segments with null two-dimensional measure

Parker Kuklinski
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Abstract

In this paper we construct an uncountable union of line segments $T$ which has full intersection with the sets $(\{ 0\} \times [0, 1]) \cup (\{ 1\} \times [0, 1])\subset\mathbb{R}^2$ but has null two-dimensional measure. Further results are proved on the decay rate of $\mu (T)$ if the line segments comprising $T$ are replaced with increasingly fine approximations by parallelograms.

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Parker Kuklinski. 2023-11-27. An uncountable union of line segments with null two-dimensional measure. https://arxiv.org/abs/2311.16210

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