Measure is a fundamental concept of mathematics. Measures provide a mathematical abstraction for common notions like mass, distance/length, area, volume, probability of events, and — after some adjustments — electrical charge. These seemingly distinct concepts are innately very similar and may, in many cases, be treated as mathematically indistinguishable. Measures are foundational in probability theory. Far-reaching generalizations of measure are widely used in quantum physics and physics in general.
The intuition behind this concept dates back to Ancient Greece, when Archimedes tried to calculate the area of a circle. But it was not until the late 19th and early 20th centuries that measure theory became a branch of mathematics. The foundations of modern measure theory were laid in the works of Émile Borel, Henri Lebesgue, Johann Radon, Constantin Carathéodory, and Maurice Fréchet, among others.