Inverse Laplace transform

In mathematics, the inverse Laplace transform of a function F(s) is the piecewise-continuous and exponentially-restricted real function f(t) which has the property:

where denotes the Laplace transform.

It can be proven that, if a function F(s) has the inverse Laplace transform f(t), then f(t) is uniquely determined (considering functions which differ from each other only on a point set having Lebesgue measure zero as the same). This result was first proven by Mathias Lerch in 1903 and is known as Lerch's theorem.