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Measurable cardinalA cardinal number κ is called measurable iff there exists a κ-additive, non-trivial, 0-1-valued measure on the power set of κ.Equivalently, κ is measurable if it is the critical point of a non-trivial elementary embedding of the universe V into a transitive class M. 
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This article is licensed under the GNU Free Documentation License. It uses material from the Wikipedia article "Measurable cardinal".