Pan-operations structure

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.