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This paper analyzes a distributed outlier detection mechanism for wireless sensor networks. Outliers are data produced by sensors which are corrupted in a way that cannot simply be explained by the effects of the measurement noise. The outlier detection mechanism assumes some generic test to be available, which is only able to determine whether a set of data contains outliers, without being able to determine which data are outliers. The focus of this paper is on the equilibrium and stability analysis of the proposed iterative distributed outlier detection mechanism. Some sufficient conditions to be satisfied by the generic outlier detection test are established. Simulation results are then provided for an outlier model.