{"paper":{"title":"A limit theorem for selectors","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Francisco Durango, Jos\\'e L. Fern\\'andez, Mar\\'ia J. Gonz\\'alez, Pablo Fern\\'andez","submitted_at":"2014-07-17T13:48:11Z","abstract_excerpt":"Any (measurable) function $K$ from $\\mathbb{R}^n$ to $\\mathbb{R}$ defines an operator $\\mathbf{K}$ acting on random variables $X$ by $\\mathbf{K}(X)=K(X_1, \\ldots, X_n)$, where the $X_j$ are independent copies of $X$. The main result of this paper concerns selectors $H$, continuous functions defined in $\\mathbb{R}^n$ and such that $H(x_1, x_2, \\ldots, x_n) \\in \\{x_1,x_2, \\ldots, x_n\\}$. For each such selector $H$ (except for projections onto a single coordinate) there is a unique point $\\omega_H$ in the interval $(0,1)$ so that for any random variable $X$ the iterates $\\mathbf{H}^{(N)}$ acting "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1407.4666","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"}