$$  \[ch0teo0\] Let $\nu_0$ be a known Lévy measure concentrated on a (possibly infinite) interval $I\subseteq {\ensuremath {\mathbb{R}}}$ and having strictly positive density with respect to the Lebesgue measure. Let us choose a parameter space ${\ensuremath {\mathscr{F}}}^{\nu_0, I}$ such that there exist a sequence $m = m_n$ of integers, functions $V_j$, $j = \pm 0, \dots, \pm m$ and a sequence $\varepsilon_m \to 0$ as $m \to \infty$ such that Conditions [(H0), (C0), (C0