Questions related to measures, sigma-algebras, measure spaces, Lebesgue integration and the like.
The modern notion of measure, developed in the late 19th century, is an extension of the notions of length, area or volume. A measure $\mu$ is a law which assigns numbers $\mu(A)$ to certain subsets $A$ of a given space and is a natural generalization of the following notions: 1) length of an interval, 2) area of a plane figure, 3) volume of a solid, 4) amount of mass contained in a region, 5) probability that an event from $A$ occurs, etc.
It originated in real analysis and is used now in many areas of mathematics, including geometry, probability theory, dynamical systems, functional analysis, etc.
Reference: Measure Theory