Measure Theory

Measure theory is a branch of mathematics that extends the concept of "size" or "volume" of sets beyond simple shapes. In calculus and analysis, it provides a rigorous framework to define and analyze quantities such as length, area, and probability. Measure theory helps us understand how to assign a consistent measure to more complex sets, enabling the integration of functions over these sets. It forms the foundation for many areas in mathematics, including probability theory and functional analysis, allowing us to work with infinite and abstract sets in a coherent way.