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/