  The theory of random sets is demonstrated to prove useful for the theory of
random operators. A random operator is here defined by requiring the graph to
be a random set. It is proved that the spectrum and the set of eigenvalues of
random operators are random sets. These results seem to be a novelty even in
the case of random bounded operators. The main technical tools are given by the
measurable selection theorem, the measurable projection theorem, and a
characterisation of the spectrum by approximate eigenvalues of the operator and
the adjoint operator. A discussion of some of the existing definitions of the
concept of a random operator is included at the end of the paper.
  Keywords: Random operators; Set-valued functions; General topics in linear
spectral theory; Random operators and equations; Stochastic integrals;
Disordered systems
