Abstract

The followingsandwich problem is considered: Given two real-valued functionsg:X→ℝ,h:Y→ℝ defined on subsetsX, Y ⊆ S of a preordered abelian monoids (S, +, 0, ≺), does there exist a real-valued ≺ additive functionf:S→ℝ such thatg≤f|X andf|Y≤h? We study several necessary conditions for the existence of such a functionf, some of which are also sufficient.

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