[KSCI] Korea Science Citation Index Service

http://dx.doi.org/10.4134/JKMS.2016.53.2.315

SATURATED STRUCTURES FROM PROBABILITY THEORY

Song, Shichang (Department of Mathematics School of Science Beijing Jiaotong University)

Publication Information

Journal of the Korean Mathematical Society / v.53, no.2, 2016 , pp. 315-329 More about this Journal

Abstract

In the setting of continuous logic, we study atomless probability spaces and atomless random variable structures. We characterize ${\kappa}$ -saturated atomless probability spaces and ${\kappa}$ -saturated atomless random variable structures for every infinite cardinal ${\kappa}$ . Moreover, ${\kappa}$ -saturated and strongly ${\kappa}$ -homogeneous atomless probability spaces and ${\kappa}$ -saturated and strongly ${\kappa}$ -homogeneous atomless random variable structures are characterized for every infinite cardinal ${\kappa}$ . For atomless probability spaces, we prove that ${\aleph}_1$ -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.

Keywords

continuous logic; saturation; Maharam spectrum; probability algebras; random variables;

Citations & Related Records

Times Cited By KSCI : 1 (Citation Analysis)

Reference
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