Gaussian measure

In mathematics, Gaussian measure is a Borel measure on finite-dimensional Euclidean space ${\displaystyle R^{n}}$, closely related to the normal distribution in statistics. There is also a generalization to infinite-dimensional spaces. Gaussian measures are named after the German mathematician Carl Friedrich Gauss. One reason why Gaussian measures are so ubiquitous in probability theory is the central limit theorem. Loosely speaking, it states that if a random variable ${\displaystyle X}$ is obtained by summing a large number ${\displaystyle N}$ of independent random variables with variance 1, then ${\displaystyle X}$ has variance ${\displaystyle N}$ and its law is approximately Gaussian.