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Completeness is a property in statistics that allows for the estimation of parameters in a probability distribution based on sample statistics. It ensures that distributions for different parameter values can be estimated accurately. In this context, the statistic theta cap is considered complete if, for every measurable function h independent of theta, the expected value is 0 implies all events where h's value is 0 have a probability of 1. This highlights the importance of measurability in statistics.
