A Product on Lorenz Hulls, Zonoids, and Vector Measure Ranges
A Lorenz hull is the convex hull of the range of an $n$-dimensional vector of finite signed measures defined on a common measurable space. We show that the set of $n$-dimensional Lorenz hulls is endowed with a natural product that is commutative, associative, and distributive over Minkowski sums. Th...
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| creator | Steinberger, John Zhang, Zhe |
| description | A Lorenz hull is the convex hull of the range of an $n$-dimensional vector of
finite signed measures defined on a common measurable space. We show that the
set of $n$-dimensional Lorenz hulls is endowed with a natural product that is
commutative, associative, and distributive over Minkowski sums. The same holds
with "zonoid" in place of "Lorenz hull" as the two concepts give rise to the
same set of subsets of $\mathbb{R}^n$. The product is defined via the common
notion of a product measure. |
| doi_str_mv | 10.48550/arxiv.2309.09790 |
| format | Article |
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finite signed measures defined on a common measurable space. We show that the
set of $n$-dimensional Lorenz hulls is endowed with a natural product that is
commutative, associative, and distributive over Minkowski sums. The same holds
with "zonoid" in place of "Lorenz hull" as the two concepts give rise to the
same set of subsets of $\mathbb{R}^n$. The product is defined via the common
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finite signed measures defined on a common measurable space. We show that the
set of $n$-dimensional Lorenz hulls is endowed with a natural product that is
commutative, associative, and distributive over Minkowski sums. The same holds
with "zonoid" in place of "Lorenz hull" as the two concepts give rise to the
same set of subsets of $\mathbb{R}^n$. The product is defined via the common
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finite signed measures defined on a common measurable space. We show that the
set of $n$-dimensional Lorenz hulls is endowed with a natural product that is
commutative, associative, and distributive over Minkowski sums. The same holds
with "zonoid" in place of "Lorenz hull" as the two concepts give rise to the
same set of subsets of $\mathbb{R}^n$. The product is defined via the common
notion of a product measure.</abstract><doi>10.48550/arxiv.2309.09790</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Mathematics - Dynamical Systems Mathematics - Probability |
| title | A Product on Lorenz Hulls, Zonoids, and Vector Measure Ranges |
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