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A class of negative definite kernels is defined in terms of measure spaces.Using this concept, property (T) for a countable group $\G$ is characterized interms of measure preserving actions of $\G$, as follows. If a set $S$ istranslated a finite amount by any fixed element of $\G$, then there is auniform bound on how far $S$ is translated.

Negative definite functions and a dynamical characterization of property (T) for countable groups