Product of uniform measures

Abstract

For i = (1, 2), let X i be Hausdorff uniform spaces and µ i uniform measures on X i . We determine the existence of the product uniform measure µ 1 ⊗ µ 2 on X 1 × X 2 and prove a Fubini type theorem and a continuity property. The result is extended to vector-valued uniform measures.Keywords Uniformly bounded equicontinuous sets · Tight measures · Inductive tensor product of locally convex spaces Mathematics Subject Classification (2000) 28A35 · 60B05 · 46G10 · 28C15 · 28B05