We consider properties of medians as they pertain to the continuity and vanishing oscillation of a function. Our approach is based on the observation that medians are related to local sharp maximal functions restricted to a cube of ℝⁿ.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-3-3, author = {Jonathan Poelhuis and Alberto Torchinsky}, title = {Medians, continuity, and vanishing oscillation}, journal = {Studia Mathematica}, volume = {209}, year = {2012}, pages = {227-242}, zbl = {1277.42024}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-3-3} }
Jonathan Poelhuis; Alberto Torchinsky. Medians, continuity, and vanishing oscillation. Studia Mathematica, Tome 209 (2012) pp. 227-242. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-sm213-3-3/