What is Initial value theorem?

In mathematical analysis, the initial value theorem is a theorem used to relate frequency domain expressions to the time domain behavior as time approaches zero.

It is also known under the abbreviation IVT.

Let

be the Laplace transform of ƒ. If f {\displaystyle f} is bounded on {\displaystyle } = O {\displaystyle f=O} ] and lim t → 0 + f {\displaystyle \lim _{t\to 0^{+}}f} exists then the initial value theorem says