Before revision:  As a byproduct of our isometry theorem, we prove that the convolution distance is closed, and also give c}(}\textbf{  some explicit examples of computation of the convolution distance.
After revision:  As a byproduct of our isometry theorem, we prove that the convolution distance is closed, and also give c}(}\textbf{ _\mathbb{R some explicit examples of computation of the convolution distance.