We consider a Köthe space of random variables (r.v.) defined on the Lebesgue space ([0,1],B,λ). We show that for any sub-σ-algebra ℱ of B and for all r.v.’s X with values in a separable finitely compact metric space (M,d) such that d(X,x) ∈ for all x ∈ M (we then write X ∈ (M)), there exists a median of X given ℱ, i.e., an ℱ-measurable r.v. Y ∈ (M) such that for all ℱ-measurable Z. We develop the basic theory of these medians, we show the convergence of empirical medians and we give some applications.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-6,
author = {Nacereddine Belili and Henri Heinich},
title = {Median for metric spaces},
journal = {Applicationes Mathematicae},
volume = {28},
year = {2001},
pages = {191-209},
zbl = {1006.60001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-6}
}
Nacereddine Belili; Henri Heinich. Median for metric spaces. Applicationes Mathematicae, Tome 28 (2001) pp. 191-209. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-am28-2-6/