Random Measures and Integrals

A random measure $Z$ is a vector-valued mapping from a $\delta$-ring to $L^p(P)$, $p>0$, and countable additivity is understood in terms of the range metric. Properties of $Z$ which need not have finite Vitali variation are considered. These include independent and/or orthogonal (if $p=2$) valued measures and their properties for shift invariant properties, and their integrals with a view to represent stochastic processes as integrals relative to such measures will be discussed. A few applications are included.