Let $g$ be Riemann integrable on $[a,b]$, $f(x)=\int_a^xg(t)dt$ for $x∈[a,b]$.
How to show that the total variation of $f$ is equal to $∫_a^b|g(x)|dx$?
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1$\begingroup$ I think it's good to mention that this is also posted on Math SE: math.stackexchange.com/questions/150579/… $\endgroup$– Dylan MorelandCommented May 31, 2012 at 5:58
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$\begingroup$ But all the Answers on SE have bug. $\endgroup$– LeitingokCommented May 31, 2012 at 6:07
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