Content (measure theory)
Encyclopedia
In mathematics
, a content is a real function
defined on a field of sets 
such that
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.
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
, a content is a real function
defined on a field of sets such that
A very important type of content is a measure
Measure (mathematics)
In mathematical analysis, a measure on a set is a systematic way to assign to each suitable subset a number, intuitively interpreted as the size of the subset. In this sense, a measure is a generalization of the concepts of length, area, and volume...
, which is a σ-additive
Sigma additivity
In mathematics, additivity and sigma additivity of a function defined on subsets of a given set are abstractions of the intuitive properties of size of a set.- Additive set functions :...
content defined on a σ-field. Every measure is a content, but not vice-versa.