Tuesday, August 22, 2006
Continuity of Probability (for monotone sets)
The idea here is to construct a sequence of disjoint, increasing (or decreasing) sets whose union is equivalent to the union of the original sequence of increasing (or decreasing) sets so that one can apply the third axiom of probability (i.e., countable additivity).
Some concepts needed to understand this proof:
De Morgan's Laws
Probability Axioms (Ignore additivity as it is a special case of countable additivity.)