Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system.

Then
\begin{equation}
T^{-1} \emptyset = \emptyset
\end{equation}

Result R4467
on D2841: Stationary measurable set

Empty set is a stationary measurable set

Formulation 0

Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system.

Then
\begin{equation}
T^{-1} \emptyset = \emptyset
\end{equation}

Proofs

Let $M = (X, \mathcal{F}, \mu, T)$ be a D2827: Measure-preserving system.

This result is a consequence of the results

$\square$

(i) | R4466: Whole space is a stationary measurable set |

(ii) | R4437: Complement of stationary measurable set is stationary |

$\square$