Let, $f:[a,b]\to[c,d]$ be a strictly increasing function. Then, obviously it is differentiable almost everywhere. Now, consider the set $S=\{x\in [a,b]: f'(x)\text{ exists and }=0\}$, then does this implies $|f(S)|=0?$
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Let, $f:[a,b]\to[c,d]$ be a strictly increasing function. Then, obviously it is differentiable almost everywhere. Now, consider the set $S=\{x\in [a,b]: f'(x)\text{ exists and }=0\}$, then does this implies $|f(S)|=0?$