If $T_1(X)$ and $T_2(X)$ are minimal sufficient statistics, does there (always) exist a bijective function g, s.t. $T_1(X)=T_2(X)$?
I think that this may be true, as they both have the minimal information about the statistical model s.t. it is sufficient. Therefore, should contain the same number of data points, which are about the same information.