A measure-theoretic Grothendieck inequality

In this note we develop a notion of integration with respect to a bimeasure μ that allows integration of functions in the projective tensor product L 2 ( ν 1 ) ⊗ ˆ L 2 ( ν 2 ) , where ν 1 and ν 2 are Grothendieck measures for μ. This integral, which agrees with the standard notion of integration with respect to a bimeasure, allows us to integrate inner products and provides a generalization of the Grothendieck inequality to a measure-theoretic setting.