I denote that a reward vector of an item $a$ as $r_a$. Say there is a set of items denoted as $A_t$. I want to get a set $A^\prime_t$ of items from $A_t$ that has non-dominated reward vectors. For a given two items $m, n$, if $n$ has a reward vector that is non-dominating I denote it as $r_m \nsucc r_n$. Is it correct to formally write $A^\prime_t$ as,

$A^\prime_t \gets \{\forall n \in A_t| \forall m \in A_t , r_m \nsucc r_n\}$

Is there a better way to write this formally?


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