Product of lattice-valued measures on topological spaces

Abstract

Abstract X1 and X 2 are completely regular Hausdorff spaces, E 1, E 2 and F are Dedekind complete Banach lattices, 〈·,·〉: E 1 × E 2 → F is a bilinear mapping, and μ 1 and μ 2 are, respectively, E 1 and E 2 valued positive, countably additive Baire or Borel measures (countable additivity relative to order convergence) on X 1 and X 2. Under certain conditions the existence and uniqueness of the F-valued, positive, product measure is proved.