[This paper][1] defines the class of sampling problems **SampP** (see Definition 11). It requires that the probability of the generated samples $C_x$ is close to the target probability $D_x$ within an error $\epsilon$. The definition of this admissible error is:
$$ \lVert C_s - D_x \rVert \le \epsilon $$
Now, what I do not clearly understand is what this norm is: $L_1$, $L_2$, or something else? It is not stated. There are passages relying on the triangular inequality, so I can tell that it must refer to some norm that has a triangle inequality. Do you have any suggestion?

  [1]: https://arxiv.org/abs/1009.5104