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In the current paper, we generalize the "compact operator" part of theVoiculescu's non-commutative Weyl-von Neumann theorem on approximateequivalence of unital $*$-homomorphisms of an commutative C$^*$ algebra$\mathcal{A}$ into a semifinite von Neumann algebra. A result of D. Hadwin forapproximate summands of representations into a finite von Neumann factor$\mathcal{R}$ is also extended.

A note on the Voiculescu's theorem for commutative C$^*$-algebras in semifinite von Neumann algebras