 Global Normality and Dominance If \(\mathfrak{I}\) is a legitimate global inaccuracy measure, there is a strictly increasing \(f:[0, \infty) \rightarrow [0, \infty)\) such   \[\mathfrak{I}(c, w) = f(||v_w - c||_2).\] where, for any two credence   functions \(c\), \(c'\) defined on \(\mathcal{F}\),   \[||c - c'||_2 := \sqrt{\sum_{X \in \mathcal{F}} |c(X) - c'(X)|^2}\]   and we call \(||c - c'||_2\) the Euclidean distance between \(c\) and \(c'\); and, recall, \(v_w\) is the omniscient credence function at \(w\), so that \(v_w(X) = 1\) if \(X\) is true at \(w\) and \(v_w(X) = 0\) if \(X\) is false at \(w\).