Author:
Boboc N.,Constantinescu C.,Cornea A.
Abstract
In the frame of the recent axiomatic theories of harmonic functions [2], [3], [1], it has been shown that the continuous bounded functions on the boundaries of relatively compact open sets are resolutive [5], [1]. The aim of the present paper is to substitute in these results the continuous functions by Borel-measurable functions and to leave out the restriction that the open sets are relatively compact. H. Bauer has replaced the axiom 3 of Brelot’s axiomatic by two weaker axioms: the axiom of separation (Trennungsaxiom) and the axiom K1. Since the axiom of separation is not fulfilled in some important cases (e.g. the compact Riemann surfaces) we shall weaken this axiom too, substituting it by one of its consequences: the minimum principle for hyperharmonic functions.
Publisher
Cambridge University Press (CUP)
Reference5 articles.
1. Axiomatique des fonctions harmoniques et surharmoniques dans un espace localement compact;Brelot;Séminaire de Théorie du Potentiel,1959
2. Axiomatische Behandlung des Dirichletschen Problems f�r elliptische und parabolische Differentialgleichungen
3. Étude comparée de quelques axiomatiques des fonctions harmoniques et surharmoniques;Brelot;Séminaire de Theorie du Potentiel,1962
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