Tag Info

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 $\mu$ 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