Let $T_1\colon [0,1]\rightarrow [0,1]$ be the full tent map, $B_1$ be the collection of Borel sets, and $m_1$ denote the Lebesgue measure. Let $T_2\colon\sum_2^+\rightarrow \sum_2^+$ be the full one sided shift map on two symbols, $B_2$ be the $\sigma$-algebra generated by cylinder sets and $m_2$ be the $(\frac{1}{2},\frac{1}{2})$ product measure. Are $T_1$ and $T_2$ isomorphic and why?
Thank you for your help.