Levy's distributional property for symmetric Levy processes

We present the Levy’s distributional property for symmetric Levy processes with generating triplet $(0,0,\nu )$ or $(\sigma >0,\gamma ,\nu )$ where $\nu$ is a symmetric measure on $R\mathrm{\backslash }\{0\}$. This generalizes the classical Levy’s theorem about Brownian motions with drift.