= Piecewise continuous function
= Piecewise continuity
{synonym}
A <function> is piecewise continuous on a finite <interval> if it is <continuous> between finitely many breakpoints and has finite <one-sided limits> at those points and at the endpoints. On $[0,\infty)$, require this on every finite <interval>. A <Heaviside step function> is an example; a <function> with an infinite blow-up at an interior point is not. This condition guarantees local <integrability> while allowing jumps in an input.
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