Measure theory is a mathematical framework that deals with the concept of measuring sets and their properties. This branch of mathematics is also known as the theory of measures, which studies the size or extent of a set. Another synonym for measure theory is the doctrine of measures, which establishes the rules and principles for measuring different kinds of objects or phenomena. Measure theory is also related to probability theory, the theory of integration, and the theory of probability distributions. In conclusion, measure theory is a central field of modern mathematics, which encompasses a wide range of topics and applications in various fields of science and engineering.