An Avoidance Principle with an Application to the Asymptotic Behaviour   of Graded Local Cohomology
  We present an Avoidance Principle for certain graded rings. As an application we fill a gap in the proof of a result by Brodmann, Rohrer and Sazeedeh about the antipolynomiality of the Hilbert-Samuel multiplicity of the graded components of the local cohomology modules of a finitely generated module over a Noetherian homogeneous ring with two-dimensional local base ring. 
M. Brodmann, S. Kurmann, F. Rohrer