{"paper":{"title":"On processes which cannot be distinguished by finitary observation","license":"","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Michael Hochman, Yonatan Gutman","submitted_at":"2006-08-13T07:15:51Z","abstract_excerpt":"A function $J$ defined on a family $C$ of stationary processes is finitely observable if there is a sequence of functions $s_n$ such that $s_n(x_1 ... x_n)\\to J(X)$ in probability for every process $X=(x_n)\\in C$. Recently, Ornstein and Weiss roved the striking result that if $C$ is the class of aperiodic ergodic finite valued processes, then the only finitely observable isomorphism invariant on $C$ is entropy. We sharpen this in several ways. Our main theorem is that if $X \\to Y$ is a zero-entropy extension of finite entropy ergodic systems and $C$ is the family of processes arising from $X$ "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/0608310","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"}