Product characterization of weak mixing
= Product characterization of weak mixing
If $T$ is weakly mixing, then $T\times S$ is ergodic exactly when $S$ is ergodic. In particular, ergodicity of $T\times T$ is equivalent to weak mixing of $T$.
= Product characterization of weak mixing
If $T$ is weakly mixing, then $T\times S$ is ergodic exactly when $S$ is ergodic. In particular, ergodicity of $T\times T$ is equivalent to weak mixing of $T$.