Given a uniform commutative associative binary operator construed as addition, A = (: a-> ((|A:)| b-> a+b :A) :), also known as `addition on' (|A:), and any relation U, `an A-measure on U' is a mapping ({relations V: U subsumes V}: m :A) for which:

- m(V&unite;W) +m(V&intersect;W) = m(V) + m(W)

From measures I should eventually be able to obtain integration: Lesbesgue did a very good job, which I shall but shadow.

The particular example which bears on my attention to this is when A is the restriction of composition to scalings on some collection U, on which an addition is defined, along with a natural embedding (at least one way or the other) between the scalings composed by A and the scalings of U.

Written by Eddy.