Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The robustness of the generalized Gini index   In this paper we introduce a map $\Phi$, which we call \textit{zonoid map},
from the space of all non-negative, finite Borel measures on $\mathbb{R}^n$
with finite first moment to the space of zonoids of $\mathbb{R}^n$. This map,
connecting Borel measure theory with zonoids theory, allows us to slightly
generalize the Gini volume introduced, in the contest of Industrial Economics,
by Dosi, Grazzi, Marengo and second author in 2016. This volume, based on the
geometric notion of zonoid, is introduced as a measure of heterogeneity among
firms in an industry and turned out to be quite interesting index as it is a
multi-dimensional generalization of the well known and broadly used Gini index.
By exploiting the mathematical contest offered by our definition, we prove the
continuity of the map $\Phi$ which, in turns, allows to prove the validity of a
Glivenko-Cantelli theorem for our generalized Gini index and, hence, for the
Gini volume. Both results, continuity of $\Phi$ and Glivenko-Cantelli theorem,
are particularly useful when dealing with a huge amount of multi-dimensional
data.

5
The categories of this paper are: gr-qc
11
The categories of this paper are: hep-lat
17
The categories of this paper are: q-fin
27
The categories of this paper are: comp-gas
26
The categories of this paper are: bayes-an
7
The categories of this paper are: hep-th
29
The categories of this paper are: funct-an
4
The categories of this paper are: cond-mat
22
The categories of this paper are: chao-dyn
8
The categories of this paper are: hep-ex
36
The categories of this paper are: cmp-lg
30
The categories of this paper are: q-alg
37
The categories of this paper are: supr-con
0
The categories of this paper are: hep-ph
23
The categories of this paper are: solv-int
24
The categories of this paper are: dg-ga