A D18: Map $f : X \to Y$ is a

**measurable space isomorphism**from $M_X$ to $M_Y$ if and only if

(1) | $f$ is a D201: Measurable map from $M_X$ to $M_Y$ |

(2) | $f$ is an D976: Invertible map with an D216: Inverse map $f^{-1} : Y \to X$ |

(3) | $f^{-1}$ is a D201: Measurable map from $M_Y$ to $M_X$ |