The Grothendieck inequality revisited

The classical Grothendieck inequality is viewed as a statement about representations of functions of two variables over discrete domains by integrals of two-fold products of functions of one variable. An analogous statement is proved, concerning continuous functions of two variables over general topological domains.The main result is the construction of a continuous map φ from l2 (A) into L2 (Ω A, PA), where A is a set, ΩA = {-1,1}A, and PA is the uniform probability measure on ΩA.