 Final value theorem

In mathematical analysis, the final value theorem (FVT) is one of several similar theorems used to relate frequency domain expressions to the time domain behavior as time approaches infinity.Mathematically, if formula_1 in continuous time has (unilateral) Laplace transform formula_2 then a final value theorem establishes conditions under which
Likewise, if formula_4 in discrete time has (unilateral) Z-transform formula_5 then a final value theorem establishes conditions under which

An Abelian final value theorem makes assumptions about the time-domain behavior of formula_1 (or formula_4) to calculate formula_9.