Kolmogorov-Sinai Entropy/Examples/Identity Mapping

Example of Kolmogorov-Sinai Entropy

Let $\struct {X, \BB, \mu}$ be a probability space.

Let $I_X: X \to X$ be the identity mapping.

Then $I_X$ is $\mu$-preserving and:

$ \map h {I_X} = 0$

where $\map h {I_X} $ is the entropy with respect to $I_X$.

Proof

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