 The definition of the continuum field necessarily uses some abstract machinery, since it does not exist as a random height function.Instead, it is a random generalized function, or in other words, a distribution on distributions (with two different meanings of the word "distribution").Given a domain Ω ⊆ R"n", consider the Dirichlet inner product

for smooth functions "ƒ" and "g" on Ω, coinciding with some prescribed boundary function on formula_8, where formula_9 is the gradient vector at formula_10.