Tensor valuations on Sobolev spaces

Tian Gao; Dan Ma

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arXiv · 2609.37580

Tensor valuations on Sobolev spaces

Tian Gao·Dan Ma

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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.

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Tian Gao, Dan Ma. 2026-09-29. Tensor valuations on Sobolev spaces. https://arxiv.org/abs/2609.37580

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