Ring of sets

In mathematics, there are two different notions of a ring of sets, both referring to certain families of sets. In order theory, a nonempty family of sets ${\displaystyle {\mathcal {R}}}$ is called a ring (of sets) if it is closed under intersection and union. That is, the following two statements are true for all sets ${\displaystyle A}$ and ${\displaystyle B}$,

In measure theory, a ring of sets ${\displaystyle {\mathcal {R}}}$ is instead a nonempty family closed under unions and set-theoretic differences. That is, the following two statements are true for all sets ${\displaystyle A}$ and ${\displaystyle B}$ (including when they are the same set),

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