{"paper":{"title":"Nearly hyperharmonic functions and Jensen measures","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2017-05-15T14:37:00Z","abstract_excerpt":"Let $(X,\\mathcal H)$ be a $\\mathcal P$-harmonic space and assume for simplicity that constants are harmonic. Given a numerical function $\\varphi$ on $X$ which is locally lower bounded, let \\begin{equation*}\n  J_\\varphi(x):=\\sup\\{\\int^\\ast \\varphi\\,d\\mu(x)\\colon \\mu\\in \\mathcal J_x(X)\\}, \\qquad x\\in X, \\end{equation*} where $\\mathcal J_x(X)$ denotes the set of all Jensen measures $\\mu$ for $x$, that is, $\\mu$ is a compactly supported measure on $X$ satisfying $\\int u\\,d\\mu\\le u(x)$ for every hyperharmonic function on $X$. The main purpose of the paper is to show that, assuming quasi-universal m"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.05269","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"}