I read in Boyd's text that over convex $C$ such a distribution:
$f(x) = {1\over a} I_C(x)$
for $I$ the indicator function for $C$ and $a$ the measure of $C$. And that taking $\log 0 = -\infty$ we have that $\log f$ is $-\log a$ for $x \in C$ and $-\infty$ otherwise. Then the text asserts that because this is concave the distribution is log concave. But isn't $-\log x$ a convex function? (Second derivative is $1/x^2$ which is always positive). I keep thinking it should be log convex, what am I missing?