Nigel Kalton and Stephen Montgomery-Smith, Set-functions and factorization. Arch. Math. 61, (1993), 183-200. If \(\phi\) is a submeasure satisfying an appropriate lower estimate we give a quantitative result on the total mass of a measure \(\mu\) satisfying \(0\le \mu \le \phi\). We give a dual result for supermeasures and then use these results to investigate convexity on non-locally convex quasi-Banach lattices. We then show how to use these results to extend some factorization theorems due to Pisier to the setting of quasi-Banach spaces. We conclude by showing that if \(X\) is a quasi-Banach space of cotype two then any operator \(T:C(\Omega) \to X\) is 2-absolutely summing and factors through a Hilbert space and discussing general factorization theorems for cotype two spaces. (tex, dvi, ps, pdf. The tex file also requires vanilla.sty.)


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