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

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 in terms of measure preserving actions of $\G$, as follows. If a set $S$ is translated a finite amount by any fixed element of $\G$, then there is a uniform bound on how far $S$ is translated.

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