{"paper":{"title":"Integral representation of linear functionals on function spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Mehdi Ghasemi","submitted_at":"2014-03-27T09:27:47Z","abstract_excerpt":"Let $A$ be a vector space of real valued functions on a non-empty set $X$ and $L:A\\rightarrow\\mathbb{R}$ a linear functional. Given a $\\sigma$-algebra $\\mathcal{A}$, of subsets of $X$, we present a necessary condition for $L$ to be representable as an integral with respect to a measure $\\mu$ on $X$ such that elements of $\\mathcal{A}$ are $\\mu$-measurable. This general result then is applied to the case where $X$ carries a topological structure and $A$ is a family of continuous functions and naturally $\\mathcal{A}$ is the Borel structure of $X$. As an application, short solutions for the full a"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1403.6956","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"}