Random fields are stochastic processes whose arguments vary continuously over some subset of Rn n-dimensional Euclidean space. They can be strictly defined on a measure space (Ω,F,P) where Ω is a set with generic element!, F F is a σ_-algebra of subsets of , and P is a probability measure on F satisfying the following axioms:
0<P(A)<1 1 and P(Ω)=1
if ; and 0 is the empty set.
Definition 1: A second order random field over is a function