Abstract
The structure of pan-addition ⊕ and pan-multiplication ⊙ of a commutative isotonic semiring ( R +, ⊕, ⊙) is analyzed. We show that if ⊕ ≠ V (supremum), then ( R +, ⊕, ⊙ ) is a g-semiring, i.e. a⊕ b = g −1( g( a) + g( b)) and d a⊙ b = g −1( g( a) · g( b)). Conclusions for pan-integrals with respect to a ⊕-measure are shown.
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