F_sigma Set

A subset  of the real numbers is said to be an  set provided  is the countable union of closed sets. The name  comes from French: The F stands for fermé, meaning "closed," while the  stands for somme, meaning "sum."

This definition is dual to that of a Gdelta set in the sense that  is an  set if and only if its complement  is a .

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.