CALCULATION OF THE SHANNON INFORMATION

Let (Ω, β, μX) and (v{inverted}, F, μN) be probability spaces, with f: Ω × v{inverted} ⇒ v{inverted} a β × F|F measurable map. Define μXY on β × F by μXY(A) = μX ⊗ μN{(x, y): (x, f(x, y)) ε{lunate} A}, and let μY = (μX ⊗ μN)o f-1. An expression is determined for computing the Shannon information in the measure μXY. This expression is used to compute the information for the non-linear additive Gaussian channel, and can be used to solve the channel capacity problem. © 1979.