Abstract:For $i=(1,2)$, let $X_{i}$ be completely regular Hausdorff spaces, $E_{i}$ quasi-complete locally convex spaces, $E=E_{1}\Breve {\otimes }E_{2}$, the completion of the their injective tensor product, $C_{b}(X_{i})$ the spaces of all bounded, scalar-valued continuous functions on $X_{i}$, and $\mu _{i}$ $E_{i}$-valued Baire measures on $X_{i}$. Under certain conditions we determine the existence of the $E$-valued product measure $\mu _{1}\otimes \mu _{2}$ and prove some properties of these measures.
Keywords: injective tensor product, product of measures, tight measures, $\tau $-smooth measures, separable measures, Fubini theorem
AMS Subject Classification: Primary 46E10, 28C05, 28C15, 46G10, 60B05; Secondary 46A08, 28B05