= Decay of a nonnegative uniformly continuous integrable function
{title2=$f\geq0,\ \int_0^\infty f<\infty\Longrightarrow f(t)\to0$}
A nonnegative uniformly continuous function on $[0,\infty)$ with finite integral tends to zero. Otherwise uniform continuity gives disjoint intervals of a fixed width on which the function exceeds a fixed positive value, contradicting integrability. This supplies a useful dissipation argument for <Lyapunov functions> with merely continuous vector fields.
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