Neil A. Watson, Department of Mathematics and Statistics, University of Canterbury, Christchurch, New Zealand, e-mail:N.Watson@math.canterbury.ac.nz

**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

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