  We introduce a concept of asymptotic principal values which enables us to
handle rigorously singular integrals of higher-order poles encountered in the
computation of various quantities based on correlation functions of a vacuum.
Several theorems on asymptotic principal values are proved and they are
expected to become bases for investigating and developing some class of
regularization methods for singular integrals. We make use of these theorems
for analyzing mutual relations between some regularization methods, including a
method naturally derived from asymptotic principal values. It turns out that
the concept of asymptotic principal values and the theorems for them are quite
useful in this type of analysis, providing a suitable language to describe what
is discarded and what is retained in each regularization method.
