ABSTRACT
Here and in Chapters 9 and 10, we deal with function µ, called measure, which returns area, or volume, or probability, of a given set. We assume that µ is already defined, adopting an axiomatic approach which turns out advantageous, as the same theoretical results apply to other situations, besides area in ℝ2 or volume in ℝ3, and which is particularly fruitful in Probability theory. A general domain that can be assumed for µ is a σ–algebra, defined in § 8.1. For completeness, a few basic concepts are recalled, for which some familiarity is assumed.
