It is well known in abstract
quantum mechanics, that when two observables have a joint distribution, a
state can be found, in which both observables have a small variance. In
order to consider a converse of this, a relation between two observables is
defined. Say x and y are two observables and that when α is a state such
that the variance of x in α is small implies the variance of y in α will be
small. From the above relation it follows that there is a continuous function
f, such that f maps the spectrum of x onto the spectrum of y. Further,
y = f(x).
