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Set functions satisfying if $f(X) \le f(Y)$ and $Z \cap (X \cup Y) = \emptyset$, then $f(X \cup Z) \le f(Y \cup Z)$
I am investigating set functions $f : 2^\Omega \to \mathbb{N}$ satisfying the following two properties:
(monotone) For all $X, Y \subset \Omega$, if $X \subseteq Y$, then $f(X) \le f(Y)$.
(property ...
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