  The Hofer-Zehnder theorem states that almost every hypersurface in a
thickening of a hypersurface $S$ in a symplectic manifold $(M,\omega)$ carries
a closed characteristic provided that $S$ bounds a compact submanifold and
$(M,\omega)$ has finite capacity. We show that it is enough to assume that the
thickening of $S$ has finite capacity.
