Pseudo-optimal measures

Based on a pseudo-addition ⊕ on [0, ∞], pseudo-optimal measures related to non-negative set functions vanishing at the empty set (non-negative games) are introduced. For a fixed pseudo-addition ⊕, an equivalence ∼⊕ on non-negative set functions is studied. A special stress is given to pure pseudo-optimal measures, admitting no other ∼⊕ equivalent set function.