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.
If $G_1$ and $G_2$ are open subset of [a,b] then $|G_1|+|G_2|=|G_1 \cup G_2|+|G_1 \cap G_2|$
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real-analysis
measure-theory
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1What does $|G|$ mean? – 2012-08-18
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0My answer assumes he means Lebesgue measure or Jordan content. – 2012-08-18
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0yes it is Lebesgue measure. – 2012-08-18
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0It has to be only a measure in a more general way. – 2012-08-18