G_delta Set

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.

REFERENCES:

Royden, H. L. and Fitzpatrick, P. M. Real Analysis. Pearson, 2010.