Abstract
A set function is a real function defined on a collection of subsets of an underlying measurable space. In this chapter we consider set functions that have some of the properties ascribed to area. The main property is additivity. The area of two regions that do not overlap is the sum of their areas. A charge is any nonnegative set function that is additive in this sense. A measure is a charge that is countably additive. That is, the area of a sequence of disjoint regions is the infinite series of their areas. A probability measure is a measure that assigns measure one to the entire set. Charges and measures are intimately entwined with integration, which we take up in Chapter 9. But here we study them in their own right.KeywordsPairwise DisjointBanach LatticeRiesz SpaceSigned ChargeMeasurable CardinalThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
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