  The determination of the time averages of continuous functions, or discrete
time sequences is important for various problems in physics and engineering,
and the generalized final-value theorems of the Laplace and z-transforms,
relevant to functions and sequences not having a limit at infinity, can be very
helpful in this determination. In the present contribution, we complete the
proofs of these theorems and extend them to more general time functions and
sequences with a well-defined average. Besides formal proofs, some simple
examples and heuristic and pedagogical comments on the physical nature of the
limiting processes defining the averaging are given.
