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Let A_+ be the ring of Laplace transforms of complex Borel measures on R withsupport in [0,+\infty) which do not have a singular nonatomic part. We comparethe nu-metric d_{A_+} for stabilizable plants over A_+ given in the article byBall and Sasane [2010], with yet another metric d_{H^\infty}|_{A_+}, namely theone induced by the metric d_{H^\infty} for the set of stabilizable plants overH^\infty given in teh article by Sasane in 2011. Both d_{A_+} and d_{H^\infty}coincide with the classical Vinnicombe metric defined for rational transferfunctions, but we show here by means of an example that these two possibleextensions of the classical nu-metric for plants over A_+ do not coincide onthe set of stabilizable plants over A_+. We also prove that they neverthelessgive rise to the same topology on stabilizable plants over A_+, which in turncoincides with the gap metric topology.

On two natural extensions of Vinnicombe's metric: their noncoincidence yet equivalence on stabilizable plants over A_+