  In this paper a general theorem of constructing infinite particle systems of
jump types with long range interactions is presented. It can be applied to the
system that each particle undergoes an $\alpha$-stable process and interaction
between particles is given by the logarithmic potential appearing random matrix
theory or potentials of Ruelle's class with polynomial decay. It is shown that
the system can be constructed for any $\alpha \in (0, 2)$ if its equilibrium
measure $\mu$ is translation invariant, and $\alpha$ is restricted by the
growth order of the 1-correlation function of the measure $\mu$ in general
case.
