{"paper":{"title":"Swap-invariant and exchangeable random measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS","math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Felix Nagel","submitted_at":"2016-02-24T20:29:28Z","abstract_excerpt":"In this work we analyze the concept of swap-invariance, which is a weaker variant of exchangeability. A random vector $\\xi$ in $\\mathbb{R}^n$ is called swap-invariant if $\\,{\\mathbf E}\\,\\big| \\!\\sum_j u_j \\xi_j \\big|\\,$ is invariant under all permutations of $(\\xi_1, \\ldots, \\xi_n)$ for each $u \\in \\mathbb{R}^n$. We extend this notion to random measures. For a swap-invariant random measure $\\xi$ on a measure space $(S,\\mathcal{S},\\mu)$ the vector $(\\xi(A_1), \\ldots, \\xi(A_n))$ is swap-invariant for all disjoint $A_j \\in \\mathcal{S}$ with equal $\\mu$-measure. Various characterizations of swap-i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1602.07666","kind":"arxiv","version":3},"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"}