  In this paper we investigate the image size characterization problem. We show
that any arbitrary source set may be decomposed into sets whose image size
characterization is the same as its entropy characterization. We also show that
the number of these sets required is small enough that one may consider that
from a coding perspective the achievable entropy region and achievable exponent
region are equal. This has an impact on many source networks and network
problems whose solution heretofore could not have the image size
characterization applied to them.
