Definition of Area of a Two Dimensional Line
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I learned recently that lines such as the boundary of some Julia sets and the Hilbert curve have area. I was wondering what the strict definition of such an area would be, and I intuitively came up with the following: Let $S$ be the set of all points on the line. Let $R$ be the set of points in some contiguous region containing the line fully inside of it. The area of the line is the percent of $R$ also in $S$ multiplied by the area of the region.
fractals
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asked Dec 27 '18 at 17:56
William Grannis
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