Definition:Measure (Measure Theory)

Definition
Let $\struct {X, \Sigma}$ be a measurable space.

Let $\mu: \Sigma \to \overline \R$ be a mapping, where $\overline \R$ denotes the set of extended real numbers.

Also see

 * Equivalence of Definitions of Measure (Measure Theory)


 * Sigma-Algebra Contains Empty Set


 * Measure of Empty Set is Zero: $\map \mu \O = 0$.
 * Measure is Finitely Additive Function


 * Definition:Lebesgue Measure
 * Definition:Measure Space


 * Characterization of Measures