Let $X$ be a compact metric space,$T$ a transformation on $X$ and $f_n$ a sequence of continuous subadditive functions $X \to \mathbb{R}$.
Des $f_n$ converge pointwise for every $x$? By kingsman subadditive Ergodic theorem the convergence is guaranteed for any regular point of an invariant measure. So if every point in $X$ is regular for some invariant measure, we are done. However, I do not think this is true. Is it? Under what conditions?
Thanks!