A Generalization of the Riesz-Herglotz Theorem on Representing Measures

Peter A. Loeb
1978 Proceedings of the American Mathematical Society  
A simple construction is given that obtains maximal representing measures for positive harmonic functions on a domain W as the weak* limits of finite sums of point masses on [0, + 00]^. This new standard result, new even for the unit disk, is established for very general elliptic differential equations and domains, in fact, for a Brelot harmonic space, using nonstandard analysis.
doi:10.2307/2042218 fatcat:ptrtggh6hbh4fp7vixdf2hfaoi