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Error theory; Probability
In the setting of continuous logic, we study atomless proba- bility spaces and atomless random variable structures. We characterize Ƙ-saturated atomless probability spaces and Ƙ-saturated atomless random variable structures for every infinite cardinal Ƙ. Moreover, Ƙ-saturated and strongly Ƙ-homogeneous atomless probability spaces and Ƙ-saturated and strongly Ƙ-homogeneous atomless random variable structures are characterized for every infinite cardinal Ƙ. For atomless probability spaces, we prove that N 1-saturation is equivalent to Hoover-Keisler saturation. For atomless random variable structures whose underlying probability spaces are Hoover-Keisler saturated, we prove several equivalent conditions.
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