Year: 2026
Type: preprint
Abstract: Previsions are positively homogeneous functionals, and are generalized forms of integration functionals. We investigate previsions -- just previsions, not sublinear or superlinear previsions as in previous work. We show that every prevision can be expressed as an infimum of sublinear previsions, and as a supremum of superlinear previsions under mild conditions. This extends to homeomorphisms between spaces of previsions and certain hyperspaces over spaces of sublinear or superlinear previsions, which can also be characterized in terms of orthogonality relations, making the construction a variant of a double powerspace construction.
Source: arXiv (Cornell University)
Author: Goubault-Larrecq, Jean
Topic: Advanced Banach Space Theory
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7160916480
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