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/