Birkhoff ergodic theorem and the measure of the bad points – mathoverflow.net

Birkhoff ergodic theorem and the measure of the bad points – mathoverflow.net

In the Birkhoff ergodic theorem we have a PMPS $(X,B,\mu,T)$ and that for
any $f\in L^1(X,\mu)$ $\frac{1}{N}\sum_{n=0}^{N-1}f(T^n x)\to \int f
d\mu,$ in measure, in $L^1$-norm and $\mu$-a.e. My ...