MATHEMATICA BOHEMICA, Vol. 130, No. 1, pp. 1-18, 2005

A Nevanlinna theorem for superharmonic functions on Dirichlet regular Greenian sets

Neil A. Watson

Neil A. Watson, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand, e-mail:

Abstract: A generalization of Nevanlinna's First Fundamental Theorem to superharmonic functions on Green balls is proved. This enables us to generalize many other theorems, on the behaviour of mean values of superharmonic functions over Green spheres, on the Hausdorff measures of certain sets, on the Riesz measures of superharmonic functions, and on differences of positive superharmonic functions.

Keywords: Nevanlinna theorem, superharmonic function, $\delta$-subharmonic function, Riesz measure, mean value

Classification (MSC 2000): 31B05, 31B10

Full text available as PDF (smallest), as compressed PostScript (.ps.gz) or as raw PostScript (.ps).

Access to the full text of journal articles on this site is restricted to the subscribers of Myris Trade. To activate your access, please contact Myris Trade at

[Next Article] [Contents of This Number] [Contents of Mathematica Bohemica]
[Full text of the older issues of Mathematica Bohemica at DML-CZ]