ThmDex – An index of mathematical definitions, results, and conjectures.

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

Proof 0

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

This result is a consequence of the results

(i)	R4466: Whole space is a stationary measurable set
(ii)	R4437: Complement of stationary measurable set is stationary

$\square$