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This paper 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 rule out the possibility that the definition holds for (whatever norm)(EDITED: functions not fulfilling the triangular equality). Do you have any suggestion?

This paper 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?

This paper 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 rule out the possibility that the definition holds for whatever norm. Do you have any suggestion?

This paper 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 rule out the possibility that the definition holds for (whatever norm)(EDITED: functions not fulfilling the triangular equality). Do you have any suggestion?

This paper 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 rule out the possibility that the definition holds for whatever norm. Do you have any suggestion?

This paper 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 rule out the possibility that the definition holds for whatever norm. Do you have any suggestion?