Concavity of the logarithm
= Concavity of the logarithm
{title2=$(\log s)''=-1/s^2<0$}
The <logarithm> is <strictly concave> on positive real numbers, as its second <derivative> is negative. Thus the <Jensen inequality> gives $\int\log f\,d\mu\le\log\int f\,d\mu$ for a <probability measure> and an integrable positive $f$, whenever the left side is defined. It also controls the negative logarithmic part of <convex> combinations of strictly positive functions.