This paper is a continuation of the authors’ paper [“The Fubini theorem for bornological product measures”, Results Math. 54, No. 1–2, 65–73 (2009; Zbl 1184.46043)]. Here, are Hausdorff complete bornological locally convex spaces with filtering upwards bases of bornologies , respectively; here, each is a closed, absolutely convex bounded subset of and a fixed closed, absolutely convex bounded subset of . The subspace of generated by , with Minkowski functional of , is a Banach space . The topology of is the inductive limit topology of the Banach spaces . Similar properties hold for the topologies of arising from respectively. is the space of all continuous linear functions from to ; similarly for and .
are two sets, and are -rings on and , respectively, and and are two measures. With the help of , the authors reduce the study from complete bornological locally convex spaces to the Banach spaces . Under certain conditions, an existence theorem for the product measure is proved. Then under certain conditions, a Fubini type theorem is proved for this product measure.