High Quality Content by WIKIPEDIA articles! High Quality Content by WIKIPEDIA articles! In mathematics, a measure-preserving dynamical system is an object of study in the abstract formulation of dynamical systems, and ergodic theory in particular. A measure-preserving dynamical system is defined as a probability space and a measure- preserving transformation on it. In more detail, it is a system (X, mathcal{B}, mu, T) with the following structure: X is a set, mathcal B is a - algebra over X, mu:mathcal{B}rightarrow[0,1] is a probability measure, so that (X) = 1, and, T:Xrightarrow X is a measurable transformation which preserves the measure , i. e. each Ain mathcal{B} satisfies mu(T^{-1}A)=mu(A).,

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