Random measure

In probability theory, a random measure is a measure-valued random element. Let X be a complete separable metric space and the σ-algebra of its Borel sets. A Borel measure μ on X is boundedly finite if μ(A) < ∞ for every bounded Borel set A. Let be the space of all boundedly finite measures on . Let (Ω, ℱ, P) be a probability space, then a random measure maps from this probability space to the measurable space (,).A measure generally might be decomposed as: