{"paper":{"title":"Nonlinear probability. A theory with incompatible stochastic variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["stat.TH"],"primary_cat":"math.ST","authors_text":"Gunnar Taraldsen","submitted_at":"2017-06-21T07:42:17Z","abstract_excerpt":"In 1991 J.F. Aarnes introduced the concept of quasi-measures in a compact topological space $\\Omega$ and established the connection between quasi-states on $C (\\Omega)$ and quasi-measures in $\\Omega$. This work solved the linearity problem of quasi-states on $C^*$-algebras formulated by R.V. Kadison in 1965. The answer is that a quasi-state need not be linear, so a quasi-state need not be a state. We introduce nonlinear measures in a space $\\Omega$ which is a generalization of a measurable space. In this more general setting we are still able to define integration and establish a representatio"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.06770","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}