  Motivated by applications to the study of stochastic processes, we introduce
a new analysis of positive definite kernels $K$, their reproducing kernel
Hilbert spaces (RKHS), and an associated family of feature spaces that may be
chosen in the form $L^{2}\left(\mu\right)$; and we study the question of which
measures $\mu$ are right for a particular kernel $K$. The answer to this
depends on the particular application at hand. Such applications are the focus
of the separate sections in the paper.

Functional Analysis;Probability