Just Previsions
2026-05-11 • Logic in Computer Science
Logic in Computer Science
AI summaryⓘ
The authors study a type of mathematical function called previsions, which generalize the idea of integration. They focus on regular previsions, unlike some earlier studies that looked at special cases called sublinear or superlinear previsions. The authors show that any prevision can be described as the lowest point of some sublinear previsions or the highest point of some superlinear previsions under certain conditions. They also explore connections between spaces of previsions and related mathematical structures, using concepts like orthogonality and double powerspaces.
previsionsublinear previsionsuperlinear previsionpositive homogeneityintegration functionalinfimumsupremumhomeomorphismorthogonalitydouble powerspace
Authors
Jean Goubault-Larrecq
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.