Given that Laplace Transform and Z-Transform are closely related, I wonder if there's a way to deduce Z-Transform final value theorem:
$$\lim_{n\rightarrow \infty} f[n] = \lim_{z \rightarrow 1}(1-z^{-1}) F(z)$$
from Laplace Transform final value:
$$\lim_{t\rightarrow \infty} f(t) = \lim_{s\rightarrow 0} sF(s)$$
and Z-Transform initial value theorem:
$$f[0] = \lim_{z \rightarrow \infty} F(z)$$
from Laplace-Transform initial value theorem:
$$f(0) = \lim_{s\rightarrow \infty} sF(s)$$