Abstract
Let (E, ≦) be a vector lattice and E + be the set of all nonnegative elements of E. We investigate M-functionals from E + into ℝ+, that is functions A: E + → ℝ+ such that $$ \Lambda (f \vee g) = \Lambda (f) \vee \Lambda (g),\Lambda (\alpha f) = \alpha \Lambda (f) $$ for α ≧ 0 and f, g ɛ E +.
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