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PreprintCC BY 4.0arXiv

Just Previsions

  • Jean Goubault-Larrecq
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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.

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Cite

BibTeXRIS
BibTeX
@misc{goubaultlarrecq2026just,
  title = {{Just Previsions}},
  author = {Jean Goubault-Larrecq},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2605.10173},
  eprint = {2605.10173},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2605.10173},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Just Previsions
AU  - Jean Goubault-Larrecq
PY  - 2026
DA  - 2026/10/20
PB  - arXiv
DO  - 10.48550/arxiv.2605.10173
UR  - https://arxiv.org/abs/2605.10173
AB  - 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.
ER  -