I read the theorem stated below on Wikipedia (http://en.wikipedia.org/wiki/Ergodicity#Formal_definition). But I do not understand how to prove the equivalence of these different definitions.Any hints are welcome. Thanks.
while trying to prove that 1 implies 2 i am given a set $E$ whose symmetric difference with $T(E)$ is of measure zero. So i wanted to find a set $F=E \cup N$ where $N$ is a null set such that $T(F)=F$. But i am unable to find such a set. Any help would be appreciated.
Thanks