Minimum measure sets (MMSs) summarize the information of a (single-class) dataset. In many situations, they can be preferred to estimated probability density functions (pdfs): they are strongly related to pdf level sets while being much easier to estimate in large dimensions. The main contribution of this paper is a theoretical connection between MMSs and one class Support Vector Machines. This justifies the use of one-class SVMs in the following applications: novelty detection (we give explicit convergence rate) and change detection.