The function which is equal to one at the rational points and to zero at the irrational points. It is also defined by the formula:
and belongs to the second Baire class (cf. Baire classes). It is not Riemann integrable on any segment but, since it is equal to zero almost-everywhere, it is Lebesgue integrable.
|||I.P. Natanson, "Theorie der Funktionen einer reellen Veränderlichen" , H. Deutsch , Frankfurt a.M. (1961) (Translated from Russian)|
Dirichlet-function. Encyclopedia of Mathematics. URL: http://encyclopediaofmath.org/index.php?title=Dirichlet-function&oldid=12889