The algebra generated by two sets

Topic: Probability spaces and events · more questions on this topic
Two series of events ›

Let \Omega=\{1,2,3,4\}, A=\{1,2\}, and B=\{2,3\}. List \sigma(A,B).

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The four atoms are A\cap B=\{2\}, A\cap B^c=\{1\}, A^c\cap B=\{3\}, and A^c\cap B^c=\{4\}. Every singleton is an atom, so every subset of \Omega is a union of atoms. Thus \sigma(A,B) is the power set of \{1,2,3,4\}.