Abstract
AbstractLetTbe a continuoust-norm (a suitable binary operation on[0, 1]) and Δ+the space of distribution functions which are concertratede on [0,∞. theτTproduct of anyF, Gin Δ+is defined at any realxby, and the pair (Δ+, τT) forms a semigroup. Thus, given a sequence {Fi} in Δ+, then-fold product τT(F1…Fn) is well-defined for eachn. Moreover, that resulting sequence {τT(F1, …,Fn)} is pointwise non-increasing and hence has a weak limit. This paper establishes a convergence theorem which yields a representation for this weak limit. In addition, we prove the Zero-One law that, for Archimedeant-norms, the weak limit is either identically zero or has supremum 1.
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