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A subset of the real numbers is said to be a set provided is the countable intersection of open sets. The name comes from German: The G stands for Gebiet, meaning "area," while the stands for Durchschnitt, meaning "intersection."
This definition is dual to that of an Fsigma set in the sense that is a set if and only if its complement is an .
Note that both and sets are fundamental to measure theory. In particular, both types of sets are Borel sets and are considered to be the second level of the so-called Borel hierarchy.
Royden, H. L. and Fitzpatrick, P. M. Real Analysis. Pearson, 2010.
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