For example, consider \(f(x) = \abs{x}\), which is differentiable everywhere except \(x=0\). If the distribution of \(X\) is continuous, \(f\) would be differentiable almost everywhere, because \(\Pr(X=0) = 0\). However, if \(X\) has a discrete distribution with positive mass at 0, \(f\) would not be differentiable almost everywhere. The “almost everywhere” claim depends on both the condition and the probability space.