One aim of the theory of probability is the effective computation, perhaps
only approximate, of probabilities that are given in principle. Of course
there are other aims, for example the creation of an effective tool for think-
thinking in a probabilistic way about physical problems and other applications, and
also the development of an aesthetically satisfying theory that ties together
the results of probabilistic computations for a particular class of structures,
for example sums of independent random variables. Here I shall be concerned
almost exclusively with a single approach to the approximate computation of
probabilities and, more generally, expectations. This work may be thought of
as an attempt to say something not entirely trivial about the approximate
computation of expectations at an abstract level. I have tried, without
complete success, to keep in mind the interaction of abstract ideas and
concrete problems.