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F_sigma Set


An F_sigma set is a subset F subset= R of the real numbers that is the union of a countable set of closed sets. The name F_sigma comes from French: The F stands for fermé, meaning "closed," while the sigma stands for somme, meaning "sum."

This definition is dual to that of a Gdelta set in the sense that F is an F_sigma set iff its complement F^c=R-F is a Gdelta set.

Both F_sigma sets and Gdelta sets are fundamental to measure theory. In particular, both types of sets are Borel sets and belong to the second level of the Borel hierarchy.


See also

Borel Hierarchy, Borel Set, Closed Set, Gdelta Set, Open Set

This entry contributed by Christopher Stover

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References

Royden, H. L. and Fitzpatrick, P. M. Real Analysis, 4th ed. Boston, MA: Pearson-Prentice Hall, 2010.

Referenced on Wolfram|Alpha

F_sigma Set

Cite this as:

Weisstein, Eric W., with contributions by Christopher Stover. "F_sigma Set." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/F-SigmaSet.html

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