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A Kakeya needle set cannot be of measure zero (a line segment cannot be rotated continuously within a set of measure 0). See the blog post by Terry Tao. However, there are sets of measure zero within which a line segment can be rotated by a Baire-1 map (link). |
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A Kakeya needle set cannot be of measure zero. See the blog post by Terry Tao. However, there are sets of measure zero within which a line segment can be rotated by a Baire-1 map (link). |
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The answer is: no A Kakeya needle set cannot be of measure zero. See the blog post by Terry Tao. |
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