A measure space is a mathematical structure used in the field of measure theory, which is a branch of mathematics that studies sizes and probabilities. It consists of a set, a σ-algebra (a collection of subsets), and a measure function that assigns a non-negative value to each set in the σ-algebra. This framework allows for the rigorous definition of concepts like length, area, and volume. In a measure space, the measure function must satisfy certain properties, such as countable additivity, which means that the measure of a union of disjoint sets equals the sum of their measures. This concept is essential for understanding integration and probability, linking it to topics like Lebesgue integration and probability theory.