In the Gaussian channel Y(t) = Φ( t) + X(t) = message + noise, where Φ( t) and X( t) are mutually independent, the information I( Y, Φ) is evaluated. One of the results is that I( Y, Φ) < ∞ if and only if Φ ϵ H ( X) = the reproducing kernel Hilbert space for X(·). And the causal formula of I( Y, Φ) is given.