  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.
