The kernel embedding of the distribution P(X) in \mathcal{H} (also called the kernel mean or mean map) is given by:[REF] .
\mu_X := \mathbb{E}_X [k(X, \cdot) ] = \mathbb{E}_X [\phi(X) ] = \int_\Omega \phi(x) \ \mathrm{d}P(x) .