The addition theorem for the entropy of transformations of 𝐺-spaces

Thomas, R. K.

doi:10.1090/S0002-9947-1971-0293064-6

The addition theorem for the entropy of transformations of $G$-spaces
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by R. K. Thomas

Trans. Amer. Math. Soc. 160 (1971), 119-130

DOI: https://doi.org/10.1090/S0002-9947-1971-0293064-6

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Abstract:

For a measure-preserving transformation $T$ which is a skew-product of a measure-preserving transformation $S$ and a topological group endomorphism $\sigma$, it is shown that the entropy $h$ satisfies the following “addition theorem": $h(T) = h(S) + h(\sigma )$.

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