J. Aust. Math. Soc.  74 (2003), 185-199
Joint continuity of injective tensor products of vector measures in Banach lattices

Jun Kawabe
  Department of Mathematics
  Faculty of Engineering
  Shinshu University
  4-17-1 Wakasato
  Nagano 380-8553

It is shown that the injective tensor product of positive vector measures in certain Banach lattices is jointly continuous with respect to the weak convergence of vector measures. This result is obtained by a diagonal convergence theorem for injective tensor integrals. Our approach to this problem is based on Bartle's bilinear integration theory.
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