forall C,B,C1,B1,.... in an algebra A,

with C1 subset C2 .... with C=union(i=1,infinity,Ci) /\ B"=>"Ci forall i
=> B "=>" C

proposition:

algebra A a sigma algebra /\ P a probability charge on A representing "=>"
=> "=>" is monotone continuous <=> P is a probability measure

(this induces finite additivity)

source

jl@crush.caltech.edu index