We study the rich behavior of ergodicity and conservativity of Cartesian products of infinite measure-preserving transformations. A class of transformations is constructed such that for any subset R aS, a"e a (c) (0, 1) there exists T in this class such that T (p) x T (q) is ergodic if and only if a R. This contrasts with the finite measure-preserving case where T (p) x T (q) is ergodic for all nonzero p and q if and only if T x T is ergodic. We also show that our class is rich in the behavior of conservative products.
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机译：我们研究了无限度量保持变换的笛卡尔积的遍历性和保守性的丰富行为。构造一类转换，使得对于任何子集R aS，“ ea（c）（0，1）”在此类中存在T，使得当且仅当R满足T（p）x T（q）时，这与有限度量保持情况相反，在这种情况下，当且仅当T x T是遍历时，T（p）x T（q）对于所有非零p和q都是遍历的。保守产品。
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