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This paper deals with countable products of countable Borel equivalence relations and equivalence relations "just above" those in the Borel reducibility hierarchy. We show that if E is strongly ergodic with respect to μ then E^N is strongly ergodic with respect to μ^N. We answer questions of Clemens and Coskey regarding their recently defined Γ-jump operations, in particular showing that the Z^2-jump of E_∞ is strictly above the Z-jump of E_∞. We study a notion of equivalence relations whicharXiv:1910.08188v1 fatcat:o7w5ygorjnagrcuwvct32i24iy