{"paper":{"title":"Distributional Compatibility for Change of Measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Bin Wang, Jie Shen, Ruodu Wang, Yi Shen","submitted_at":"2017-06-05T00:11:54Z","abstract_excerpt":"In this paper, we characterize compatibility of distributions and probability measures on a measurable space. For a set of indices $\\mathcal J$, we say that the tuples of probability measures $(Q_i)_{i\\in \\mathcal J} $ and distributions $(F_i)_{i\\in \\mathcal J} $ are {compatible} if there exists a random variable having distribution $F_i$ under $Q_i$ for each $i\\in \\mathcal J$. We first establish an equivalent condition using conditional expectations for general (possibly uncountable) $\\mathcal J$. For a finite $n$, it turns out that compatibility of $(Q_1,\\dots,Q_n)$ and $(F_1,\\dots,F_n)$ dep"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1706.01168","kind":"arxiv","version":5},"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"}