The term "classical information theory" is used in the literature, by and large, to refer to the theory based on the notion of probability (Chapter 3). Uncertainty functions in this theory are expressed in terms of classical measure theory, which in turn, is formalized in terms of classical set theory. Generalizing the concept of a classical measure is thus one way of enlarging the framework for a broader treatment of the concept of uncertainty and the associated concept of uncertainty-based information. The purpose of this chapter is to discuss this generalization. Further enlargement of the framework, which is discussed in Chapter 8, is obtained by fuzzifications of classical as well as generalized measures. Basic characteristics of both these generalizations are depicted in Figure 4.1.