2
$\begingroup$

If $G_1$ and $G_2$ are open subset of [a,b] then $|G_1|+|G_2|=|G_1 \cup G_2|+|G_1 \cap G_2|$ I have some problem to understand complete theorem. in this theorem first case is finitely many intervals reference book using $\chi$ function which have 4 cases.whenever $x \in [a,b]$ then they will directly say that $\chi$ function is Riemann integrable i don't know why?please help me.thanks in advance.

  • 1
    What does $|G|$ mean?2012-08-18
  • 0
    My answer assumes he means Lebesgue measure or Jordan content.2012-08-18
  • 0
    yes it is Lebesgue measure.2012-08-18
  • 0
    It has to be only a measure in a more general way.2012-08-18

2 Answers 2