## A generalization of the Riesz-Herglotz theorem on representing measures

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- by Peter A. Loeb PDF
- Proc. Amer. Math. Soc.
**71**(1978), 65-68 Request permission

## Abstract:

A simple construction is given that obtains maximal representing measures for positive harmonic functions on a domain*W*as the $\mathrm {weak}^*$ limits of finite sums of point masses on ${[0, + \infty ]^W}$. 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.

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## Additional Information

- © Copyright 1978 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**71**(1978), 65-68 - MSC: Primary 31D05
- DOI: https://doi.org/10.1090/S0002-9939-1978-0588522-2
- MathSciNet review: 0588522