axiom PA1 is partition axiom 1:
forall n=>2, O can be partitioned in 2^n equally likely events.
There exists {E1n,..,E2^nn} s.t. Ein intersect Ejn = empty set forall i!=j
and Union(i=1,2^n,Ein)=O with Ein ~ Ejn.
=>
* There exists no w in O s.t. w ">" empty set.
* algebra A is atomlesss.
Define K(n,A) = Union(i=1,k, Ein)"<="B
Proposition:
"=>" a qualitative probability(QP) /\ satisfies PA1 =>
* P(A)=lim(n->infinity,K(n,A)/2^n) exists
* P is a probability charge
* forall B,C in A A"=>"B => P(A)"=>"P(B)