We prove that the complement of a higher-dimensional Nikodym set must have full Hausdorff dimension.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-6,
author = {Themis Mitsis},
title = {On Nikodym-type sets in high dimensions},
journal = {Studia Mathematica},
volume = {162},
year = {2004},
pages = {189-192},
zbl = {1094.28002},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-6}
}
Themis Mitsis. On Nikodym-type sets in high dimensions. Studia Mathematica, Tome 162 (2004) pp. 189-192. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm163-2-6/