One key fact in the multiplicity theory of bounded linear normal operators on a Hilbert space is the representation of the multiplicity function n. If A is the operator of multiplication by a function a on \(L^ 2[0,1]\) (with respect to Lebesgue masure m) this is performed in a rather elementary way, which easily can be treated in a course on operator theory subsequent to the spectral theorem: For a Borel set S in [0,1] and any \(\lambda\) in the spectrum of A set \(D(S,\lambda):=\liminf m(S\cap a^{-1}(B_{\delta}(\lambda)))/m(a^{- 1}(B_{\delta}(\lambda)))\) for \(\delta\to 0\), \(\delta >0\) (where \(B_{\delta}\) is the closed disc in the complex plane with centre \(\lambda\) and radius \(\delta)\). The set \(a_ e^{-1}(\lambda)\) is defined to consist of all those \(x\in [0,1]\) such that \(D(S,\lambda)>0\) for any open neighbourhood S of x. Then n(\(\lambda)\) is the cardinality of \(a_ e^{-1}(\lambda)\) if this is a finite set and \(n(\lambda)=\infty\) if \(a_ e^{-1}(\lambda)\) is infinite.