Ergodicity of the Cartesian product

Flytzanis, Elias G.

doi:10.1090/S0002-9947-1973-0328021-6

Ergodicity of the Cartesian product
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by Elias G. Flytzanis PDF

Trans. Amer. Math. Soc. 186 (1973), 171-176 Request permission

Abstract:

${h_1}$ is an ergodic conservative transformation on a $\sigma$-finite measure space and ${h_2}$ is an ergodic measure preserving transformation on a finite measure space. We study the point spectrum properties of ${h_1} \times {h_2}$. In particular we show ${h_1} \times {h_2}$ is ergodic if and only if ${h_1} \times {h_2}$ have no eigenvalues in common other than the eigenvalue 1. The conditions on ${h_1},{h_2}$ stated above are in a sense the most general for the validity of this result.

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