Small sample spaces for Gaussian processes

It is known that the membership in a given reproducing kernel Hilbert space (RKHS) of samples Gaussian process X controlled by certain nuclear dominance condition. However, it less clear how to identify “small” set functions (not necessarily vector space) contains samples. This article presents general approach for identifying such sets. We use scaled RKHSs, which can be viewed as generalisation scales, define sample support largest contained every element full measure under law σ-algebra induced collection RKHS. potentially non-measurable then shown consist those expanded terms an orthonormal basis RKHS covariance and have their squared coefficients bounded away from zero infinity, result suggested Karhunen–Loève theorem.