Content (measure theory)

In mathematics, a content is a real function $\mu$ defined on a field of sets $\mathcal{A}$ such that

1. $\mu(A)\in\ [0, \infty] \mbox{ whenever } A \in \mathcal{A}.$
2. $\mu(\varnothing) = 0.$
3. $\mu(A_1 \cup A_2) = \mu(A_1) + \mu(A_2) \mbox{ whenever } A_1,A_2 \in \mathcal{A} \mbox{ and } A_1 \cap A_2 = \varnothing.$

A very important type of content is a measure, which is a σ-additive content defined on a σ-field. Every measure is a content, but not vice-versa.

External links

• http://statmath.wu-wien.ac.at/~strasser/STATS%2025-01-2006.pdf