{"paper":{"title":"Inconsistency of Measure-Theoretic Probability","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.GM","authors_text":"Guang-Liang Li, Victor O.K. Li","submitted_at":"2014-12-06T09:30:57Z","abstract_excerpt":"We reveal a contradiction in measure-theoretic probability. The contradiction is an \"equation\" $1/2 = 0$ with its two sides representing probabilities. Unlike known paradoxes in mathematics, the revealed contradiction cannot be explained away and actually indicates that measure-theoretic probability is inconsistent. Appearing only in the theory, the contradiction does not exist in the physical world. So practical applications of measure-theoretic probability will not be affected by the inconsistency as long as \"ideal events\" in the theory (which will never occur physically) are not mistaken fo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1412.5411","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"}