Uniqueness of the Laplace transform
= Uniqueness of the Laplace transform
If two piecewise continuous <functions> of <exponential order> on $[0,\infty)$ have the same unilateral <Laplace transform> for every sufficiently large positive real parameter, they agree at every common point of continuity and agree almost everywhere. For continuous <functions>, the equality holds everywhere. Values at an isolated discontinuity cannot be recovered from an ordinary <integral transform>.