# Measure (mathematics)

**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.

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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.