The study of definable sets and functions in polish spaces.

Becker, H. and Kechris, A. S. The Descriptive Set Theory of Polish Group Actions. New York: Cambridge University Press, 1996.

CITE THIS AS:

Weisstein, Eric W. "Descriptive Set Theory." From MathWorld--A Wolfram Web Resource. http://mathworld.wolfram.com/DescriptiveSetTheory.html