  We prove that solutions of the 3D relativistic Vlasov-Maxwell system can be
extended, as long as the quantity $\sigma_{-1}(t, x) = \max_{|\omega|=1}
\,\int_{R^3} \frac{dp}{\sqrt{1+p^2}}\, \frac{1}{(1+v\cdot\omega)}\, f(t, x, p)$
is bounded in $L^2_x$.
