Abstract

In classical ergodic theory, the behaviors of automorphisms, endomorphisms, flows, and semiflows are studied in measure spaces. Let \((\mathbb {M},\mathscr {G},\mu )\) be a measure space with a normalized measure \(\mu \). This section introduces some basic concepts concerning invariant measures and ergodicity for endomorphisms and semiflows. We refer to [53] for more details about the ergodic theory of dynamical systems in measure spaces.

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