{"paper":{"title":"Measurable events indexed by words","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.CO"],"primary_cat":"math.PR","authors_text":"Konstantinos Tyros, Pandelis Dodos, Vassilis Kanellopoulos","submitted_at":"2013-03-19T19:54:50Z","abstract_excerpt":"For every integer $k\\geq 2$ let $[k]^{<\\mathbb{N}}$ be the set of all words over $k$, that is, all finite sequences having values in $[k]:=\\{1,...,k\\}$. A Carlson-Simpson tree of $[k]^{<\\mathbb{N}}$ of dimension $m\\geq 1$ is a subset of $[k]^{<\\mathbb{N}}$ of the form \\[ \\{w\\}\\cup \\big\\{w^{\\smallfrown}w_0(a_0)^{\\smallfrown}...^{\\smallfrown}w_{n}(a_n): n\\in \\{0,...,m-1\\} \\text{ and } a_0,...,a_n\\in [k]\\big\\} \\] where $w$ is a word over $k$ and $(w_n)_{n=0}^{m-1}$ is a finite sequence of left variable words over $k$. We study the behavior of a family of measurable events in a probability space i"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1303.5001","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"}