 Strong Convexity Suppose \(\mathfrak{I}\) is a legitimate inaccuracy measure. Then if \(c \neq c'\) and \(\mathfrak{I}(c, w) = \mathfrak{I}(c', w)\), then   \[\mathfrak{I}\left(\frac{1}{2}c + \frac{1}{2}c', w\right) &lt; \mathfrak{I}(c, w) = \mathfrak{I}(c', w)\] (Given two credence  functions, \(c\) and \(c'\), we define a third credence function \(\frac{1}{2}c + \frac{1}{2} c'\) as follows: the credence that \(\frac{1}{2}c + \frac{1}{2}c'\) assigns to a proposition is the straight average of the credences that \(c\) and \(c'\) assign to it. Thus, \((\frac{1}{2}c + \frac{1}{2}c')(X) = \frac{1}{2}c(X) + \frac{1}{2}c'(X).\) We call this the equal mixture of \(c\) and \(c'\).)