In mathematical analysis, the Haar measure assigns an "invariant volume" to subsets of locally compact topological groups, consequently defining an integral for functions on those groups. This measure was introduced by Alfréd Haar in 1933, though its special case for Lie groups had been introduced by Adolf Hurwitz in 1897 under the name "invariant integral". Haar measures are used in many parts of analysis, number theory, group theory, representation theory, statistics, probability theory, and ergodic theory. == Preliminaries == Let ( G , ⋅ ...

In mathematics, a varifold is, loosely speaking, a measure-theoretic generalization of the concept of a differentiable manifold, by replacing differentiability requirements with those provided by rectifiable sets, while maintaining the general algebraic structure usually seen in differential geometry. More closely, the varifold generalize the idea of a rectifiable current. Varifolds are one of the topics of study in geometric measure theory. == Historical note == Varifolds were first introduced by L.C. Young in (Young 1951), under the name "generalized surfaces". Frederick Almgren slightly modified...