Year: 2026
Type: preprint
Abstract: A complete classification is established for continuous, SL($n$) contravariant, and translation invariant tensor valuations defined on the Sobolev space $W^{1,p}(\mathbb R^n)$. When these valuations are further assumed to be homogeneous, the classification reveals that they are precisely the Fisher information tensors, which constitute a higher-order generalization of the Fisher information matrix.
Source: arXiv (Cornell University)
Authors: Gao, Tian, Ma, Dan
Institution: Shanghai Normal University
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
Award: G9000844471
OpenAlex ID: W7214940637