  In this work we present a direct proof about radonification of a cylindrical
L\'evy process. The radonification technique has been very useful to define an
genuine stochastic process starting from a cylindrical process, this is
possible thanks to the Hilbert-Schmidt operators. With this work we want to
propose a self-contained simple proofs who those who are not familiar with this
method, and also present our result which it is apply the radonification method
to the case of a cylindrical L\'evy process.
