Somehow the prices of all assets will determine a probability measure.

A probability measure is called risk neutral if for all .

In that case the states become probability measures, as noted in the introduction.

In this definition, P is the probability measure on the sigma algebra.

It tells if and how it is possible to change from one probability measure to another.

States can be viewed as noncommutative generalizations of probability measures.

The masses have to sum to one since is a probability measure.

A probability measure is sought on this space, invariant under the symmetry group.

It is related to the existence of conditional probability measures.

Let Σ denote the set of probability measures on the real line.