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Φ-Bounded Harmonic Functions and the Classification of Harmonic Spaces
Published online by Cambridge University Press: 22 January 2016
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By a harmonic space we mean a pair (X, H) where X is a locally compact, non-compact, connected, locally connected Hausdorff space ; and H is a sheaf of harmonic functions defined as follows: Suppose to each open set Ω ⊂ X there corresponds a linear space H(Ω) of finitely-continuous real-valued functions defined on Ω. Then H = {H(Ω)}Ω must satisfy the three axioms of Brelot (1) and in addition Axiom 4 of Loeb (4): 1 is H-superharmonic in X.
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- Copyright © Editorial Board of Nagoya Mathematical Journal 1972