Gaussian measure

Summary

A Gaussian measure is a probability measure whose one-dimensional projections are all normal distributions. On $\R^n$ these are the laws of Gaussian random vectors. On infinite-dimensional spaces, such as spaces of continuous paths, Gaussian measures are the main examples of well-behaved measures, and Wiener measure is one of them. There is no translation-invariant analogue of Lebesgue measure in infinite dimensions, so Gaussian measures often take its place.