= Threshold Choquet representation in L-infinity
{title2=$H_t(s)=2\,1_{\{t\le(1+f(s))/2\}}-1$}
For a real <function> in the $L^\infty$ unit ball, push uniform <measure> on $t\in[0,1]$ forward by the displayed sign-valued <functions>. In the <weak-star topology> this is a Borel probability concentrated on the <extreme points>, and <Fubini's theorem> shows that its <barycenter> is $f$. Weak-star compactness and separability of the predual $L^1$ place the example within <Choquet theorem>.
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