4

Let $\chi$ be the characteristic function of the rational numbers in $[0,1]$. Does there exist a sequence $\{f_n\}$ of continuous functions on $[0,1]$ that converges pointwise to $\chi$?

Jonas Meyer
  • 53,602
Dave
  • 615
  • 3
    See also http://math.stackexchange.com/questions/15088/is-every-lebesgue-measurable-function-on-mathbbr-the-pointwise-limit-of-cont/15091#15091 and http://math.stackexchange.com/questions/4738/points-of-continuity-of-a-function-being-dense. – Jonas Meyer Sep 15 '11 at 03:54
  • 2
    The characteristic function is a classic example of the Baire class 2 http://en.wikipedia.org/wiki/Baire_function. – Andrew Sep 15 '11 at 05:30
  • 3
    Good questions here should have two additional pieces of information: where you encountered the problem, and what you have already tried. – Carl Mummert Sep 15 '11 at 10:56

0 Answers0