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

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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

$\square$