2018/09/23 by Wolfhard Hansen, Hansen, Wolfhard, Ivan Netuka +1
Mathematics · #31C05 #31D05 #60J45 #60J62 #Advanced Banach Space Theory #FOS: Mathematics #Holomorphic and Operator Theory #Mathematical Dynamics and Fractals #Probability (math.PR)
paper · pdf · doi:10.48550/arxiv.1809.08611
openalex publication_date 2018/09/23 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let \mathfrak X be a Hunt process on a locally compact space X such that the set \mathcal E\mathfrak X of its Borel measurable excessive functions separates points, every function in \mathcal E\mathfrak X is the supremum of its continuous minorants in \mathcal E\mathfrak X and there are strictly positive continuous functions v,w∈\mathcal E\mathfrak X such that v/w vanishes at infinity. A numerical function u≥ 0 on X is said to be nearly hyperharmonic, if ∫^∗ u∘ XτV dPx≤ u(x) for all x∈ X and relatively compact open neighborhoods V of x, where τV denotes the exit time of V. For every such function u, its lower semicontinous regularization u is excessive. The main purpose of the paper is to give a short, complete and understandable proof for the statement that every Borel measurable nearly hyperharmonic function on X is the infimum of its majorants in E\mathfrak X. The major novelties of our approach are the following: 1. A quick reduction to the special case, where starting at x∈ X with u(x)