In mathematics — specifically, in the fields of probability theory and inverse problems — Besov measures and associated Besov-distributed random variables are generalisations of the notions of Gaussian measures and random variables, Laplace distributions, and other classical distributions. They are particularly useful in the study of inverse problems on function spaces for which a Gaussian Bayesian prior is an inappropriate model. The construction of a Besov measure is similar to the construction of a Besov space, hence the nomenclature.