I'm struggling with this question for over a week now. I know the proposition is true, but haven't managed to prove it yet. any suggestions anyone? ($f$ is BV on $I$ if $$\sup\left\{\sum|f(b_k)-f(a_k)| :a_{k+1}\gt b_{k}\gt a_{k} ; a_k,b_k\in I\right\}\lt \infty)$$
2026-03-27 23:13:09.1774653189
How to show that every bounded variation function on $[a,b]$ is differentiable a.e?
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Every function of bounded variation is the difference of two monotonically non-decreasing functions. Monotonically non-decreasing functions are differentiable almost everywhere.