Let (phi in mathcal{L}^{1}([0,1], d x)) and define (f(t):=int_{[0,1]}|phi(x)-t| d x). Show that (i) (f) is continuous,
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Let \(\phi \in \mathcal{L}^{1}([0,1], d x)\) and define \(f(t):=\int_{[0,1]}|\phi(x)-t| d x\). Show that
(i) \(f\) is continuous,
(ii) \(f\) is differentiable at \(t \in \mathbb{R}\) if, and only if, \(\lambda\{\phi=t\}=0\).
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i ii Lett E R R for some R 0 Since px t px t px R L0 1 dx and since t pxt ...View the full answer
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