In algebra and number theory, a distribution is a function on a system of finite sets into an abelian group which is analogous to an integral: it is thus the algebraic analogue of a distribution in the sense of generalised function. The original examples of distributions occur, unnamed, as functions φ on Q/Z satisfying Such distributions are called ordinary distributions. They also occur in p-adic integration theory in Iwasawa theory. for some weight function w. The family φ is then a distribution on the projective system X.