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I'm having a lot of trouble getting my head around this problem

For a map: $A:\left((s\left[ a,b\right] ;\mathbb{R} \right) , \left\| \cdot \right\|_{\infty }) \rightarrow \left( \mathbb{R}, \left| \cdot \right| \right)$ which maps a step function $s$ to $A\left( s\right) =\int ^{b}_{a}\left| s\left( t\right) \right| dt$

How would I be a able to describe the set of those step function so $s\in S\left( \left[ a,b\right] ;\mathbb{R} \right)$ where A is Frechet differentibale

I've been trying for a while, but I don't really know where to start. Any help would be appreciated thanks

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    I would suggest that your function should be at least not equal to zero almost everywhere, since the zero part is alsways non-differentiable. – 2017-02-13

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