For almost every tent map, the turning point is typical

Let ${\displaystyle T_a}$ be the tent map with slope a. Let c be its turning point, and ${\displaystyle {\mu }_a}$ the absolutely continuous invariant probability measure. For an arbitrary, bounded, almost everywhere continuous function g, it is shown that for almost every a, ${\displaystyle ʃgd{\mu }_a=\underset{n\to \infty }{lim}\frac{1}{n}{\sum }_{i=0}^{n-1}g(T^i\_a\left(c\right))}$. As a corollary, we deduce that the critical point of a quadratic map is generically not typical for its absolutely continuous invariant probability measure, if it exists.