The Laplace functional of a random measure 
is the functional
![L_X(f)=E[exp(-intfdX)],](/images/equations/LaplaceFunctional/NumberedEquation1.svg) |
defined for suitable nonnegative measurable functions 
. It is called a functional because its
argument is the entire function 
, rather than a number. It generalizes the Laplace
transform of a random variable and, under
standard conditions, determines the probability law
of the random measure. Conditional Laplace functionals
are obtained by taking the expected value conditional
on specified initial data or another event.
