{"paper":{"title":"Quasi-invariance of countable products of Cauchy measures under non-unitary dilations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.ST","stat.TH"],"primary_cat":"math.PR","authors_text":"Han Cheng Lie, T. J. Sullivan","submitted_at":"2016-11-30T17:50:25Z","abstract_excerpt":"Consider an infinite sequence $(U_n)_{n\\in\\mathbb{N}}$ of independent Cauchy random variables, defined by a sequence $(\\delta_n)_{n\\in\\mathbb{N}}$ of location parameters and a sequence $(\\gamma_n)_{n\\in\\mathbb{N}}$ of scale parameters. Let $(W_n)_{n\\in\\mathbb{N}}$ be another infinite sequence of independent Cauchy random variables defined by the same sequence of location parameters and the sequence $(\\sigma_n\\gamma_n)_{n\\in\\mathbb{N}}$ of scale parameters, with $\\sigma_n\\neq 0$ for all $n\\in\\mathbb{N}$. Using a result of Kakutani on equivalence of countably infinite product measures, we show t"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1611.10289","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"}