# Nikodym Set

**URL:** <https://boards.straightdope.com/t/nikodym-set/731447>\
**Category:** Factual Questions\
**Created:** [September 16, 2015, 5:16am UTC](https://boards.straightdope.com/t/nikodym-set/731447 "2015-09-16T05:16:31Z")\
**Posts on this page:** 2\
**Page:** 1

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**Author:** ![ricksummon](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/ricksummon/32/3333_2.png) [@ricksummon](https://boards.straightdope.com/u/ricksummon)\
**Post date:** [September 16, 2015, 5:16am UTC](https://boards.straightdope.com/t/nikodym-set/731447/1 "2015-09-16T05:16:31Z")

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The [Nikodym set](https://en.wikipedia.org/wiki/Nikodym_set) is a mathematical subset of the unit square that not only has the same area as the unit square, but every point in the set has a straight line that can be drawn through it without intersecting any other points in the set.

Unfortunately, that’s about all the Wikipedia article has to say about it. Where can I find a proof that this set exists? I assume it’s one of those sets that is non-constructible.

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**Author:** ![Lance\_Turbo](https://sea3.discourse-cdn.com/straightdope/user_avatar/boards.straightdope.com/lance_turbo/32/6156_2.png) [@Lance\_Turbo](https://boards.straightdope.com/u/Lance_Turbo)\
**Post date:** [September 16, 2015, 4:34pm UTC](https://boards.straightdope.com/t/nikodym-set/731447/2 "2015-09-16T16:34:22Z")

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It is constructible.

Start on page 215 [here](https://uqu.edu.sa/files2/tiny_mce/plugins/filemanager/files/4290569/13/Real%20Variable%20Methods%20in%20Fourier%20Analysis%20(North-Holland%20Mathematics%20Studies)%20(Miguel%20De%20Guzman)%200444861246.pdf).