partition axiom 2 (PA2): C,B in A s.t. C">"B => there exists {E1,..,En} of O s.t. A">"B union Ei forall i PA2 => * {w} ~ empty set * atomlessness Proposition: "=>" QP => ( PA2 <=> fine /\ tight) Theorem: "=>" QP /\ PA2 <=> there exists P on (O,2^O) s..t * A"=>"B <=> P(A)=>P(B) * forall A in 2^O, forall v in [0,1] there exists B subset A s.t. P(B)=vP(A)