Content (measure theory)
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In mathematics, a content is a real function <math>\mu</math> defined on a field of sets <math>\mathcal{A}</math> such that
- <math>\mu(A)\in\ [0, \infty] \mbox{ whenever } A \in \mathcal{A}.</math>
- <math>\mu(\varnothing) = 0. </math>
- <math>\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.</math>
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.
