This is  Theorem 3.34 in 

<cite authors="Kallenberg, Olav">_Kallenberg, Olav_, Random measures, Berlin: Akademie-Verlag. London - New York - San Francisco: Academic Press. 104 p. M 28.00 (1976). [ZBL0345.60032](https://zbmath.org/?q=an:0345.60032).</cite>