  We give a simple Tauberian proof of the Prime Number Theorem using only
elementary real analysis. Hence, the analytic continuation of Riemann's zeta
function $\zeta$ and its non-vanishing value on the whole line $\{z\in {\mathbb
C};\,{\mathrm{Re}\,} z=1\}$ are no more required. This is achieved by showing a
strong extension for Laplace transforms on the real line of Wiener--Ikehara's
theorem on Dirichlet's series, where the Tauberian assumption is reduced to a
local boundary behavior around the pole.
