User:NikelsenH/Campbell measure

Definition
Let $$ \xi $$ be a random measure on $$ S $$ and $$ \eta $$ be a random element on $$ T $$. Then the Campbell measure $$ C_{\xi,\eta} $$ on $$ S \times T $$ is defined via
 * $$ \int f \; \mathrm d C_{\xi,\eta} = \operatorname E \left[ \int f(s,\eta) \; \xi(\mathrm ds) \right]$$,

where $$ f $$ is a positive, measurable function on $$ S \times T $$.