Equating the achievable exponent region to the achievable entropy region by partitioning the source

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.